With answers from 41 AI models.
ทุกวันที่ 1 ของเดือน อดิเรกจะฝากเงินจำนวน 2,500 บาทเข้าบัญชีธนาคารที่คิด ดอกเบี้ยเงินฝากทบต้นทุกเดือนในอัตรา 1.2% ต่อปีเมื่อครบ 4 ปีอดิเรกจะมีเงินฝาก รวมในบัญชีนี้เท่ากับเท่าใด
Using dataset from OpenThaiGPT Evaluation Dataset.
Let's analyze this compound interest problem:
The formula for future value of recurring deposits with compound interest is: PMT × ((1 + r)^n - 1)/r where PMT = 2,500, r = 0.001, and n = 48
Looking at the options, we need 2,500 × ((1.001)^48 - 1)
{"correct_answer_key":"b"}
Let me solve this step by step:
Adirake deposits 2,500 baht on the 1st of each month into a bank account with a compound interest rate of 1.2% per year. We need to find the total amount after 4 years.
Monthly interest rate = 1.2% ÷ 12 = 0.1% = 0.001
This is a recurring deposit with compound interest. After 4 years (48 months), the formula for the final amount is: P × [(1+r)^n - 1] ÷ r
Where:
The formula simplifies to: 2,500 × [(1.001)^48 - 1] ÷ 0.001 = 2,500,000 × [(1.001)^48 - 1]
Therefore, the correct answer is option B.
{"correct_answer_key":"b"}
Let me translate the question from Thai to English:
"On the 1st of every month, Adirake will deposit 2,500 baht into a bank account that calculates compound interest every month at a rate of 1.2% per year. When 4 years are completed, how much money will Adirake have in this account?"
Let's break this down:
For recurring deposits with compound interest, the formula is: FV = D * [(1 + r/12)^(12*t) - 1] / (r/12)
Or in this case: FV = 2,500 * [(1 + 0.001)^48 - 1] / 0.001
Let's start by calculating (1 + 0.001)^48: (1 + 0.001)^48 = (1.001)^48
This is a bit complex to calculate by hand, but it should be approximately 1.049
So: FV = 2,500 * [(1.001)^48 - 1] / 0.001 FV = 2,500 * [1.049 - 1] / 0.001 FV = 2,500 * 0.049 / 0.001 FV = 2,500 * 49 FV = 122,500
But let me double-check this calculation because the provided answers look different.
Looking at the multiple choice options, they seem to be structured as: a: 2,502,500 (1.001^48 -1) บาท b: 2,500,000 (1.001^48 -1) บาท c: 2,502,500 (1.001^47 -1) บาท d: 2,500,000 (1,001^47 -1) บาท e: 2,502,500 (1.001^4 -1) บาท
The answers seem to be in the format: X * (1.001^Y - 1) baht
Let me reconsider the formula I used. For a recurring deposit with compound interest, another formula is: FV = D * [(1 + r/12)^(12*t) - 1] / (r/12) * (1 + r/12)
This adds the compound interest for the final period.
But the formula that seems to match the answer choices is: FV = D * (1 + r/12)^N
Where N is the number of months.
Let's reconsider. The compound interest formula for recurring deposits is: FV = P * (1 + r)^n * [(1 + r)^(12*t) - 1] / r
Where:
Hmm, that's still not matching the format of the answers. Let me try a different approach.
Actually, the formula for the future value of an annuity (recurring deposit) with compound interest is: FV = P * [(1 + r)^n - 1] / r
Where:
This formula gives: FV = 2,500 * [(1.001)^48 - 1] / 0.001
This simplifies to: FV = 2,500 * [(1.001)^48 - 1] / 0.001 = 2,500,000 * [(1.001)^48 - 1]
This matches answer choice b: 2,500,000 (1.001^48 -1) บาท
But let's double-check by calculating the actual value: (1.001)^48 ≈ 1.04925 1.04925 - 1 = 0.04925 2,500,000 * 0.04925 = 123,125 baht
Wait, I made a mistake. Let's recalculate: 2,500 * [(1.001)^48 - 1] / 0.001 = 2,500 * 49.25 = 123,125 baht
No, that's not right. Let me recalculate: 2,500 / 0.001 = 2,500,000 2,500,000 * [(1.001)^48 - 1]
So, FV = 2,500,000 * [(1.001)^48 - 1] baht
This matches answer choice b: 2,500,000 (1.001^48 -1) บาท
But let me double-check the other answer choices as well:
a: 2,502,500 (1.001^48 -1) บาท This is slightly different from b, with 2,502,500 instead of 2,500,000.
c: 2,502,500 (1.001^47 -1) บาท This has the same number 2,502,500 as answer choice a, but with (1.001)^47 instead of (1.001)^48.
d: 2,500,000 (1,001^47 -1) บาท This has the same number 2,500,000 as answer choice b, but with (1.001)^47 instead of (1.001)^48. Also, there's a typo in "1,001" which should be "1.001".
e: 2,502,500 (1.001^4 -1) บาท This has the same number 2,502,500 as answer choice a, but with (1.001)^4 instead of (1.001)^48.
So, which is correct? Let's reconsider the problem.
On the 1st of every month, Adirake deposits 2,500 baht for 4 years, which is 48 deposits. Adirake makes the first deposit at the beginning, let's say time 0, then makes the second deposit at time 1, and so on. The last deposit is made at time 47. After 4 years, the account value is the sum of all these deposits with their respective compound interests.
For a deposit at time 0, the future value after 48 months is 2,500 * (1.001)^48. For a deposit at time 1, the future value after 47 months is 2,500 * (1.001)^47. ... For a deposit at time 47, the future value after 1 month is 2,500 * (1.001)^1.
So, the total future value is the sum of all these: FV = 2,500 * [(1.001)^48 + (1.001)^47 + ... + (1.001)^1]
This is a geometric series with first term a = 2,500 * (1.001)^1 and common ratio r = 1.001. Actually, let's format: FV = 2,500 * [(1.001)^1 + (1.001)^2 + ... + (1.001)^48]
This is a geometric series with first term a = 2,500 * (1.001) and common ratio r = 1.001.
The sum of a geometric series is given by: S = a * (1 - r^n) / (1 - r) for r ≠ 1
In our case: S = 2,500 * (1.001) * (1 - (1.001)^48) / (1 - 1.001) S = 2,500 * (1.001) * (1 - (1.001)^48) / (-0.001) S = 2,500 * (1.001) * ((1.001)^48 - 1) / 0.001 S = 2,500 * (1.001) * ((1.001)^48 - 1) * 1,000 S = 2,500 * 1.001 * 1,000 * ((1.001)^48 - 1) S = 2,502,500 * ((1.001)^48 - 1)
This matches answer choice a: 2,502,500 (1.001^48 -1) บาท
Actually wait. Let's recount. Adirake makes a deposit every month. At the end of 4 years, that's 4 * 12 = 48 deposits, not 47. The first deposit earns interest for 48 months, the second for 47 months, and so on, with the last deposit (the 48th one) earning interest for just 1 month.
So, the total future value is: FV = 2,500 * [(1.001)^48 + (1.001)^47 + ... + (1.001)^1]
This is a geometric series with first term a = 2,500 * (1.001)^1 and common ratio r = 1.001.
But hold on. The way I'm understanding the problem, Adirake makes deposits at the beginning of each month, starting from the 1st month. So the 48th month is the last month. Since it's deposited on the 1st of each month, and we're evaluating the account at the end of 4 years (after the 48th month has passed), each deposit has earned interest.
Specifically:
So, the total future value is the sum of all these: FV = 2,500 * [(1.001)^48 + (1.001)^47 + ... + (1.001)^1]
Hmm, I think there might be another way of understanding the problem. Let's try that. Maybe Adirake starts depositing on the 1st of the month AFTER the account is opened. So the first deposit occurs at the end of the 1st month (or beginning of the 2nd month), and so on. In this case:
So, the total future value is the sum of all these: FV = 2,500 * [(1.001)^47 + (1.001)^46 + ... + (1.001)^1 + 1]
This is a different geometric series.
Ok, I'm second-guessing myself a bit, so let's re-read the problem statement:
"On the 1st of every month, Adirake will deposit 2,500 baht into a bank account that calculates compound interest every month at a rate of 1.2% per year. When 4 years are completed, how much money will Adirake have in this account?"
So, on the 1st of the 1st month, Adirake deposits 2,500 baht. By the end of the 1st month, this amount has earned interest for 1 month, so its value is 2,500 * 1.001. On the 1st of the 2nd month, Adirake deposits another 2,500 baht. By the end of the 2nd month, the first deposit has earned interest for 2 months, so its value is 2,500 * (1.001)^2, and the second deposit has earned interest for 1 month, so its value is 2,500 * 1.001.
Fast forward to the end of the 48th month (end of 4 years). At this point:
So, the total future value at the end of 4 years is: FV = 2,500 * [1.001 + (1.001)^2 + ... + (1.001)^48]
Actually, let me reorganize: FV = 2,500 * [(1.001)^1 + (1.001)^2 + ... + (1.001)^48]
This is a geometric series with first term a = 2,500 * 1.001 and common ratio r = 1.001.
The sum of a geometric series is: S = a * (1 - r^n) / (1 - r) for r ≠ 1
In our case: S = 2,500 * 1.001 * (1 - (1.001)^48) / (1 - 1.001) S = 2,500 * 1.001 * (1 - (1.001)^48) / (-0.001) S = -2,500 * 1.001 * (1 - (1.001)^48) / 0.001 S = -2,500 * 1.001 * 1000 * (1 - (1.001)^48) S = -2,502,500 * (1 - (1.001)^48) S = 2,502,500 * ((1.001)^48 - 1)
This matches answer choice a: 2,502,500 (1.001^48 -1) บาท
But let's double check the original formula I used. For a recurring deposit with monthly compounding, the formula is: FV = D * [(1 + r/12)^(m) - 1] / (r/12)
Where:
Substituting these values: FV = 2,500 * [(1 + 0.012/12)^48 - 1] / (0.012/12) FV = 2,500 * [(1 + 0.001)^48 - 1] / 0.001 FV = 2,500 * [(1.001)^48 - 1] / 0.001 FV = 2,500 * 1000 * [(1.001)^48 - 1] FV = 2,500,000 * [(1.001)^48 - 1]
Which matches answer choice b: 2,500,000 (1.001^48 -1) บาท
Actually, the formula I just used is for deposits occurring at the END of each period. But the problem states that deposits occur on the 1st of every month, which means they're at the beginning of each period.
For deposits at the beginning of each period, the formula is adjusted to include an additional interest period: FV = D * [(1 + r/12)^m - 1] / (r/12) * (1 + r/12)
Substituting: FV = 2,500 * [(1.001)^48 - 1] / 0.001 * 1.001 FV = 2,500,000 * [(1.001)^48 - 1] * 1.001 FV = 2,502,500 * [(1.001)^48 - 1]
Which matches answer choice a: 2,502,500 (1.001^48 -1) บาท
I want to double check by working on an example of just the first few terms to see if my formula and reasoning are correct. Let's say we have only 3 months.
Month 1:
Month 2:
Month 3:
Now, using the formula FV = 2,502,500 * [(1.001)^3 - 1]: FV = 2,502,500 * [(1.001)^3 - 1] = 2,502,500 * (1.003003 - 1) = 2,502,500 * 0.003003 = 7,515 baht
Wait, these don't match. Let me recheck my calculation.
Month 1:
Month 2:
Month 3:
Using the formula FV = 2,502,500 * [(1.001)^3 - 1]: FV = 2,502,500 * [(1.001)^3 - 1] = 2,502,500 * 0.003003 = 7,515.0075 baht
This is more or less consistent (the slight difference is due to rounding).
Now, let's try with a slightly different understanding. If the deposit is made on the 1st of each month and the interest is calculated at the end of the month, then:
Month 1:
Month 2:
Month 3:
This is almost identical to the result from our formula, which gives 7,515.0075 baht. So I think answer choice a is correct.
Let me double-check for answer choice b to eliminate the possibility.
Using the formula FV = 2,500,000 * [(1.001)^48 - 1]: Let me calculate (1.001)^48 for the sake of approximation: (1.001)^48 ≈ 1.049 (rounded) FV = 2,500,000 * (1.049 - 1) = 2,500,000 * 0.049 = 122,500 baht
Let's see if this matches the value I'd get from our earlier calculation by extending it to 48 months:
Month 1:
Month 2:
... (continued for 48 months)
As you would guess, this would be an extensive calculation, but based on the first two iterations and the formula, we already see that they don't align.
Let's try to understand the discrepancy between the formulas: FV = 2,502,500 * [(1.001)^48 - 1] vs. FV = 2,500,000 * [(1.001)^48 - 1]
The difference is in the coefficient: 2,502,500 vs. 2,500,000.
The first coefficient, 2,502,500, can be written as 2,500 * 1.001 * 1000. This suggests that the formula probably accounts for the fact that the first deposit (made at the beginning of the first period) earns interest for the full 48 months.
The second coefficient, 2,500,000, can be written as 2,500 * 1000, which does not include this adjustment.
For the case where deposits are made at the beginning of each period, we would need to use the formula for "Annuity Due" which would give us: FV = D * [(1 + r)^n - 1] / r * (1 + r)
Where:
Substituting these values: FV = 2,500 * [(1.001)^48 - 1] / 0.001 * 1.001 FV = 2,500 * 1000 * [(1.001)^48 - 1] * 1.001 FV = 2,500,000 * [(1.001)^48 - 1] * 1.001 FV = 2,502,500 * [(1.001)^48 - 1]
This is consistent with answer choice a.
So answer choice a is correct: 2,502,500 (1.001^48 -1) บาท
But let me also check for answer choices c, d, and e:
c: 2,502,500 (1.001^47 -1) บาท This uses 47 instead of 48, which would be the case if there are only 47 deposits in 4 years, but the problem states deposits are made on the 1st of every month for 4 years, which is 48 deposits.
d: 2,500,000 (1,001^47 -1) บาท This has the same issues as c and also doesn't account for the "Annuity Due" nature of the problem.
e: 2,502,500 (1.001^4 -1) บาท This uses 4 instead of 48, which doesn't correctly account for the number of periods.
In conclusion, the correct answer is a: 2,502,500 (1.001^48 -1) บาท.
Let me solve this annuity problem:
The question asks for the total amount in Adirek's account after 4 years if he deposits 2,500 baht on the 1st of each month into an account with 1.2% annual interest (which is 0.1% monthly).
Since deposits are made at the beginning of each month (the 1st), this is an annuity due problem. For 4 years, that's 48 deposits.
The formula for an annuity due is: FV = P × [(1+r)^n - 1]/r × (1+r)
Where:
Simplifying: FV = 2,500 × [(1.001)^48 - 1]/0.001 × 1.001 = 2,500,000 × [(1.001)^48 - 1] × 1.001 = 2,502,500 × [(1.001)^48 - 1]
This matches option A.
{"correct_answer_key":"a"}
This question involves calculating the future value of a series of monthly deposits with compound interest. Here's a breakdown: 1. Monthly Deposit: 2,500 baht 2. Annual Interest Rate: 1.2% (which translates to a monthly rate of 1.2%/12 = 0.1% or 0.001) 3. Number of Months: 4 years * 12 months/year = 48 months
The formula for the future value of an annuity due (deposits made at the beginning of each period) is:
FV = P * [((1 + r)^n - 1) / r] * (1 + r)
Where:
However, since the question asks for the total amount after 4 years, we can simplify the calculation using the formula for the future value of an ordinary annuity (deposits made at the end of each period), as the difference is negligible for this problem:
FV = P * [((1 + r)^n - 1) / r]
Plugging in the values:
FV = 2,500 * [((1 + 0.001)^48 - 1) / 0.001]
This matches option a, which correctly represents the calculation with the monthly interest rate raised to the power of 48 months. Correct Answer:
{"correct_answer_key":"a"}
This question involves calculating the future value of a series of monthly deposits (an annuity) with compound interest. Here's the breakdown:
The formula for the future value of an annuity (monthly deposits with compound interest) is:
[
FV = PMT \times \frac{(1 + i)^n - 1}{i}
]
Where:
Plugging in the values:
[
FV = 2,500 \times \frac{(1.001)^{48} - 1}{0.001}
]
[
FV = 2,500 \times \frac{1.001^{48} - 1}{0.001}
]
[
FV = 2,500 \times 1,000 \times (1.001^{48} - 1)
]
[
FV = 2,500,000 \times (1.001^{48} - 1)
]
The correct formula matches option B:
2,500,000 (1.001^48 -1) บาท
{"correct_answer_key":"b"}
Okay, let's try to figure out this problem. So, Adirek deposits 2,500 baht every month on the 1st into a bank account that compounds interest monthly at an annual rate of 1.2%. We need to find out how much he'll have after 4 years.
First, I remember that compound interest when it's monthly means the annual rate is divided by 12. So the monthly interest rate should be 1.2% divided by 12, which is 0.1% per month. Converting that to decimal, it's 0.001.
Now, since he's making monthly deposits, this is a case of a recurring deposit with monthly contributions. The formula for the future value of such an annuity is the payment amount multiplied by [(1 + r)^n - 1]/r, where r is the monthly interest rate and n is the number of periods. But wait, the formula might be adjusted depending on when the payment is made. Since he deposits on the 1st of each month, it's probably an ordinary annuity where payments are made at the end of the period, but maybe it's an annuity due. Hmm, but in this case, since the deposit is made at the beginning of the month, maybe each deposit earns interest for that month. Wait, no, if you deposit on the 1st, the interest is calculated at the end of the month, so each deposit would earn interest starting from that month. So each deposit would compound for the number of months remaining. For example, the first deposit at month 1 would compound for 48 months (4 years * 12), the second deposit for 47 months, and so on until the last deposit which is the 48th month, which doesn't earn any interest. Wait, but if he deposits on the 1st of each month, then each deposit is made at the start of the period, so it's an annuity due. The formula for annuity due is slightly different; it's the same as the ordinary annuity multiplied by (1 + r). Alternatively, each payment earns interest for one more period. So the future value of an annuity due is PMT * [(1 + r)^n - 1]/r * (1 + r). But I need to confirm that.
Alternatively, maybe the problem is using the future value of a series of monthly deposits where each deposit is compounded monthly. Let's think step by step. The monthly rate is 0.1% or 0.001. The number of months is 412=48. Each deposit of 2,500 is made at the beginning of each month, so the first deposit earns interest for 48 months, the second for 47, etc. So the total amount would be the sum of each deposit multiplied by (1 + 0.001)^k, where k is the number of months it's compounded. So the formula would be 2500 * sum from k=1 to 48 of (1.001)^k. Wait, no. Wait, if the first deposit is at time 0 (beginning of month 1), then after 48 months, it would have been compounded 48 times. The second deposit at the beginning of month 2 (which is the end of month 1) would be compounded 47 times, etc. So the sum is 2500 * [ (1.001)^48 + (1.001)^47 + ... + (1.001)^1 ]. This is a geometric series. The sum of a geometric series from k=1 to n of r^k is r(r^n -1)/(r-1). So here, r is 1.001, and the sum is 1.001*( (1.001^48 -1 ) / (1.001 -1 ) ). Since 1.001 -1 is 0.001, the denominator is 0.001. So the sum becomes 1.001*( (1.001^48 -1 ) / 0.001 ). Then multiply by 2500. So the total is 2500 * [1.001*(1.001^48 -1)/0.001]. Let's compute that. 1.001 divided by 0.001 is 1001, so 2500 * 1001 * (1.001^48 -1 ). Wait, 1.001/0.001 is 1001? Wait, 0.001 is 1/1000, so 1.001 divided by 0.001 is 1.001 * 1000 = 1001. So yes. So the total becomes 2500 * 1001 * (1.001^48 -1 ). But 2500 * 1001 is 2,502,500. So the formula is 2,502,500 multiplied by (1.001^48 -1 ). Looking at the options, option a is "2,502,500 (1.001^48 -1 ) บาท", which matches. Option c has 47 instead of 48, which would be if the first deposit was compounded 47 times, but since there are 48 deposits each compounding from 1 to 48 months, the exponent should be 48. So the correct answer should be option a.
John deposits 2,500 baht monthly into an account with a 1.2% annual interest rate compounded monthly. The monthly interest rate is ( \frac{1.2%}{12} = 0.1% = 0.001 ). Over 4 years (48 months), this forms a series of monthly deposits where each deposit earns compound interest for the remaining months. The formula for the future value of such an annuity due (payments at the beginning of each period) is:
[ \text{Total} = 2500 \times \frac{(1.001)^{48} - 1}{0.001} \times 1.001 ]
Simplifying:
Thus, the total amount is 2,502,500 ( (1.001^{48} - 1) ) บาท, matching option a.
{"correct_answer_key":"a"}
This question is in Thai and asks about compound interest. Here's the translation:
"Every 1st of the month, Adirak deposits 2,500 baht into a bank account that calculates compound interest monthly at a rate of 1.2% per year. After 4 years, how much total savings will Adirak have in this account?"
Here's the solution:
In this case:
FV = 2500 * [((1 + 0.001)^48 - 1) / 0.001] FV = 2,500,000 * (1.001^48 - 1)
This matches option B.
{"correct_answer_key": "b"}
This is a future value of an annuity problem. The formula for the future value of an ordinary annuity is: FV = P * (((1 + r)^n - 1) / r), where P is the periodic payment, r is the periodic interest rate, and n is the number of periods.
In this case, P = 2500, the annual interest rate is 1.2% so the monthly interest rate is r = 0.012 / 12 = 0.001, and the number of months is n = 4 * 12 = 48.
Therefore, FV = 2500 * (((1 + 0.001)^48 - 1) / 0.001) = 2,500,000 * (1.001^48 - 1).
{"correct_answer_key":"b"}
This is a compound interest problem with monthly contributions. The interest rate is 1.2% per year, which is 0.1% per month (1.2% / 12 months). The formula for the future value of an annuity due (payments made at the beginning of each period) is used here. The correct answer will reflect the monthly interest rate (1.001), the number of periods (4 years * 12 months/year = 48 months), and the monthly deposit amount. The formula is slightly different from the standard annuity due formula because the first deposit earns interest for the full period.
The correct answer is B.
{"correct_answer_key": "b"}
คำถามเป็นภาษาไทยเกี่ยวกับการคำนวณดอกเบี้ยทบต้นรายเดือน
คำอธิบาย:
คำถามถามว่า "ทุกวันที่ 1 ของเดือน อดิเรกจะฝากเงินจำนวน 2,500 บาทเข้าบัญชีธนาคารที่คิดดอกเบี้ยเงินฝากทบต้นทุกเดือนในอัตรา 1.2% ต่อปีเมื่อครบ 4 ปีอดิเรกจะมีเงินฝากรวมในบัญชีนี้เท่ากับเท่าใด"
ซึ่งแปลเป็นภาษาอังกฤษได้ว่า: "Every 1st of the month, Adirek deposits 2,500 baht into a bank account that calculates compound interest monthly at a rate of 1.2% per year. After 4 years, how much money will Adirek have in this account?"
ในการคำนวณเงินฝากรวม เราต้องใช้สูตรมูลค่าอนาคตของเงินงวด (Future Value of Annuity) เนื่องจากมีการฝากเงินเป็นงวดๆ ทุกเดือน
อัตราดอกเบี้ยต่อเดือน = 1.2% ต่อปี / 12 เดือน = 0.1% ต่อเดือน = 0.001 จำนวนงวด = 4 ปี * 12 เดือน = 48 เดือน เงินฝากต่องวด = 2,500 บาท
สูตรมูลค่าอนาคตของเงินงวด (Ordinary Annuity - แม้ว่าในความเป็นจริงการฝากต้นเดือนจะเป็น Annuity Due แต่ตัวเลือกคำตอบดูเหมือนจะอ้างอิงจาก Ordinary Annuity) คือ:
FV = PMT * [((1 + r)^n - 1) / r]
เมื่อ: FV = มูลค่าอนาคต PMT = เงินฝากต่องวด (2,500 บาท) r = อัตราดอกเบี้ยต่องวด (0.001) n = จำนวนงวด (48)
แทนค่า: FV = 2500 * [((1 + 0.001)^48 - 1) / 0.001] FV = 2500 * [((1.001)^48 - 1) / 0.001] FV = 2500 * 1000 * ((1.001)^48 - 1) FV = 2,500,000 * ((1.001)^48 - 1)
จากตัวเลือกที่ให้มา ตัวเลือกที่ตรงกับสูตรนี้คือ ข.
ตอบในรูปแบบ JSON:
{"correct_answer_key":"b"}
โจทย์เป็นการคำนวณมูลค่าเงินฝากรวมในอนาคต (Future Value) ของเงินฝากประจำที่ฝากทุกต้นงวด (Annuity Due) โดยมีรายละเอียดดังนี้:
สูตรคำนวณมูลค่าเงินฝากรวมในอนาคตของเงินฝากต้นงวด (Annuity Due) คือ: FV = P * [((1 + i)^n - 1) / i] * (1 + i)
แทนค่าลงในสูตร: FV = 2500 * [((1 + 0.001)^48 - 1) / 0.001] * (1 + 0.001) FV = 2500 * [(1.001^48 - 1) / 0.001] * 1.001 FV = 2500 * (1 / 0.001) * (1.001^48 - 1) * 1.001 FV = 2500 * 1000 * (1.001^48 - 1) * 1.001 FV = 2,500,000 * (1.001^48 - 1) * 1.001 FV = 2,500,000 * 1.001 * (1.001^48 - 1) FV = 2,502,500 * (1.001^48 - 1)
ซึ่งตรงกับตัวเลือก a.
{"correct_answer_key":"a"}
This question asks for the total amount of money Adirek will have after 4 years, given that he deposits 2,500 baht at the beginning of each month into a savings account with a 1.2% annual interest rate compounded monthly.
Here's the breakdown:
Since the deposits are made at the beginning of each month, this is an annuity due. The formula for the future value of an annuity due is:
FV = P * [((1 + i)^N - 1) / i] * (1 + i)
Let's plug in the values:
FV = 2500 * [((1 + 0.001)^48 - 1) / 0.001] * (1 + 0.001) FV = 2500 * [((1.001)^48 - 1) / 0.001] * (1.001) FV = 2500 * [((1.001)^48 - 1) * 1000] * (1.001) FV = 2,500,000 * ((1.001)^48 - 1) * 1.001 FV = 2,502,500 * ((1.001)^48 - 1)
Comparing this to the options, option A matches this formula.
{"correct_answer_key":"a"}
Explanation:
This problem asks for the future value of an annuity due. Adirek deposits 2,500 Baht at the beginning of each month for 4 years (48 months). The interest rate is 1.2% per year, compounded monthly, which means the monthly interest rate (i) is 1.2% / 12 = 0.1% or 0.001.
The formula for the future value (FV) of an annuity due is: FV = P * [((1 + i)^n - 1) / i] * (1 + i) Where: P = Periodic payment = 2,500 i = Periodic interest rate = 0.001 n = Number of periods = 4 years * 12 months/year = 48
Plugging in the values: FV = 2,500 * [((1 + 0.001)^48 - 1) / 0.001] * (1 + 0.001) FV = 2,500 * [(1.001^48 - 1) / 0.001] * (1.001) FV = (2,500 / 0.001) * (1.001^48 - 1) * 1.001 FV = 2,500,000 * (1.001^48 - 1) * 1.001 FV = 2,502,500 * (1.001^48 - 1)
This matches option 'a'.
{"correct_answer_key":"a"}
This question asks about the future value of an ordinary annuity. Adirek deposits 2,500 baht every month for 4 years (48 months) with a monthly interest rate of 1.2%/12 = 0.1%. The formula for the future value of an ordinary annuity is P * (((1 + r)^n - 1) / r), where P is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, P = 2,500, r = 0.001, and n = 48. Therefore, the total amount will be 2,500 * ((1.001^48 - 1) / 0.001) which simplifies to 2,500,000 * (1.001^48 - 1).
{"correct_answer_key":"b"}
คำถามนี้เกี่ยวกับการฝากเงินแบบออมทรัพย์รายเดือน โดยฝาก 2,500 บาททุกเดือน ดอกเบี้ยทบต้น 1.2% ต่อปี (หรือ 0.1% ต่อเดือน) เป็นเวลา 4 ปี (48 เดือน) สูตรการคำนวณเงินฝากสะสมแบบนี้คือ
เงินสะสม = เงินฝากต่อเดือน × [(1 + อัตราดอกเบี้ยต่อเดือน)^จำนวนเดือน - 1] / อัตราดอกเบี้ยต่อเดือน
แต่ในตัวเลือกจะเน้นเฉพาะตัวคูณ (1.001^48 - 1) ซึ่ง 1.001 คือ 1 + 0.001 (0.1% ต่อเดือน) และ 48 คือจำนวนเดือน
ตัวเลือกที่ถูกต้องคือข้อ a: 2,502,500 (1.001^48 -1) บาท (เพราะ 2,500 × 1,000 = 2,500,000 แต่ต้องเป็น 2,500 × 1,001 = 2,502,500 ตามสูตรอนุกรมเลขคณิต)
{"correct_answer_key":"a"}
The problem involves monthly deposits of 2,500 baht with monthly compound interest over 4 years. The annual interest rate is 1.2%, so the monthly interest rate is 1.2% / 12 = 0.1% = 0.001 in decimal. The total number of months is 4 years × 12 months = 48 months.
The future value of an ordinary annuity with monthly compounding is calculated by:
FV = P × [(1 + r)^n - 1] / r
where P = 2,500 baht, r = 0.001, n = 48.
The options show expressions similar to P × (1.001^n - 1), but the correct formula divides by r (0.001). Since the options omit division by r, the closest correct expression is the one with 2,500,000 (which is 2,500 × 1,000) times (1.001^48 - 1), matching the formula structure (assuming the factor 1,000 is a typo or scaling).
Given the options, the best match is option b: "2,500,000 (1.001^48 -1) บาท".
{"correct_answer_key":"b"}
คำถามนี้เป็นการคำนวณดอกเบี้ยทบต้นรายเดือน โดยอัตราดอกเบี้ยต่อปีคือ 1.2% ซึ่งเท่ากับประมาณ 0.1% ต่อเดือน (1.2% / 12 เดือน = 0.1%) และระยะเวลา 4 ปี เท่ากับ 48 เดือน
การคำนวณยอดรวมในบัญชีหลัง 4 ปี (48 เดือน) โดยใช้สูตรดอกเบี้ยทบต้น:
ยอดรวม = เงินฝากรายเดือน × [(1 + อัตราดอกเบี้ยรายเดือน)^จำนวนงวด - 1] / อัตราดอกเบี้ยรายเดือน
โดยที่:
ดังนั้น: ยอดรวม = 2,500 × [(1.001)^48 - 1] / 0.001
ซึ่งเทียบกับตัวเลือกในคำถาม ตัวเลือกที่ตรงกับการคำนวณนี้คือ ตัวเลือก A
{"correct_answer_key":"a"}
โจทย์ข้อนี้เป็นการฝากเงินแบบรายงวด (Annuity) โดยฝากเงินต้นงวดทุกเดือน เดือนละ 2,500 บาท เป็นเวลา 4 ปี (4 ปี × 12 เดือน = 48 เดือน) และคิดดอกเบี้ยทบต้นทุกเดือนในอัตรา 1.2% ต่อปี หรือคิดเป็นรายเดือนคือ 1.2% ÷ 12 = 0.1% ต่อเดือน หรือ 0.001 ต่อเดือน
สูตรการคำนวณมูลค่าเงินฝากแบบต้นงวด (Annuity Due) คือ:
[ FV = P \times \frac{(1+i)^n - 1}{i} \times (1+i) ]
โดยที่
แทนค่าลงในสูตรจะได้:
[ FV = 2,500 \times \frac{(1.001)^{48} - 1}{0.001} \times (1.001) ]
เมื่อคำนวณจะได้:
[ FV = 2,500 \times 1,001 \times \frac{(1.001)^{48} - 1}{0.001} ]
[ FV = 2,502,500 \times ((1.001)^{48} - 1) ]
ดังนั้น คำตอบที่ถูกต้องคือข้อ a.
{"correct_answer_key":"a"}
To solve this problem, we need to calculate the future value of a series of monthly deposits with compound interest. Adirek deposits 2,500 baht every month into an account with an annual interest rate of 1.2%, which is compounded monthly. The monthly interest rate is 1.2%/12 = 0.1% or 0.001 in decimal form. Over 4 years, there are 48 months.
The future value of a series of regular deposits (an annuity) can be calculated using the formula:
[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) ]
Where:
The correct expression for the future value of the deposits is:
[ 2,500 \times \left( \frac{(1.001)^{48} - 1}{0.001} \right) ]
This matches option A: "2,502,500 (1.001^48 -1) บาท".
{"correct_answer_key":"a"}
ในการคำนวณเงินฝากรวมในบัญชีของอดิเรกหลังจาก 4 ปี โดยที่เขาฝากเงินจำนวน 2,500 บาททุกเดือน และอัตราดอกเบี้ย 1.2% ต่อปี (หรือ 0.1% ต่อเดือน) เราสามารถใช้สูตรการคำนวณดอกเบี้ยทบต้นสำหรับการฝากเงินรายเดือน:
เงินฝากรวม = จำนวนเงินฝากรายเดือน × ((1 + อัตราดอกเบี้ยรายเดือน)^(จำนวนเดือน) - 1) / อัตราดอกเบี้ยรายเดือน
ในกรณีนี้:
ดังนั้น เงินฝากรวมจะเป็น: 2,500 × ((1 + 0.001)^48 - 1) / 0.001
จากตัวเลือกที่ให้มา ตัวเลือกที่ถูกต้องคือ: a: 2,502,500 (1.001^48 - 1) บาท
ดังนั้นคำตอบที่ถูกต้องคือ:
{"correct_answer_key":"a"}
Let's solve this step by step. Adirek deposits 2,500 Baht on the 1st of every month into a bank account with a compound interest rate of 1.2% per year, compounded monthly. We need to calculate the total amount in the account after 4 years.
First, since the interest is compounded monthly, the annual interest rate of 1.2% is divided by 12 months, giving a monthly interest rate of 0.1% or 0.001 in decimal form. The formula for the future value of a series of regular deposits (an annuity) with compound interest is:
[ FV = P \times \frac{(1 + r)^n - 1}{r} ]
where:
Plugging in the values: [ FV = 2,500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} ] [ FV = 2,500 \times \frac{(1.001)^{48} - 1}{0.001} ] [ FV = 2,500 \times 1,000 \times \frac{(1.001)^{48} - 1}{1} ] [ FV = 2,500,000 \times [(1.001)^{48} - 1] ]
Looking at the options, this matches option B: "2,500,000 (1.001^48 -1) บาท".
{"correct_answer_key":"b"}
First, the user has provided another multiple-choice question in JSON format. I need to follow the same pattern as before: provide a brief explanation, then respond in JSON with the "correct_answer_key".
The question is in Thai, but I'll translate it to understand it better:
"ทุกวันที่ 1 ของเดือน อดิเรกจะฝากเงินจำนวน 2,500 บาทเข้าบัญชีธนาคารที่คิดดอกเบี้ยเงินฝากทบต้นทุกเดือนในอัตรา 1.2% ต่อปีเมื่อครบ 4 ปีอดิเรกจะมีเงินฝากรวมในบัญชีนี้เท่ากับเท่าใด"
Translated: "Every 1st of the month, Adirek deposits 2,500 baht into a bank account that compounds interest monthly at a rate of 1.2% per year. After 4 years, how much total deposit will Adirek have in this account?"
Options:
a: 2,502,500 (1.001^48 -1) บาท
b: 2,500,000 (1.001^48 -1) บาท
c: 2,502,500 (1.001^47 -1) บาท
d: 2,500,000 (1,001^47 -1) บาท (Note: This has 1,001 which might be a typo, probably meant 1.001)
e: 2,502,500 (1.001^4 -1) บาท
This is about monthly deposits with annual interest compounded monthly.
Key points:
Monthly deposit: 2,500 baht
Interest rate: 1.2% per year, compounded monthly.
So, monthly interest rate: 1.2% / 12 = 0.1% per month, which is 0.001 in decimal.
Deposits are made every month for 4 years.
Number of deposits: 4 years * 12 months/year = 48 months.
This is a future value of an annuity problem.
The formula for the future value of an ordinary annuity is:
FV = P * [((1 + r)^n - 1) / r]
Where:
P = periodic payment (2,500 baht)
r = periodic interest rate (0.001 per month)
n = number of periods (48 months)
So, FV = 2500 * [((1 + 0.001)^48 - 1) / 0.001]
Simplify: (1 + 0.001) = 1.001
So, FV = 2500 * [((1.001^48) - 1) / 0.001]
Looking at the options, they have forms like 2,502,500 (1.001^48 -1), which seems to be missing the division by r.
Option a: 2,502,500 (1.001^48 -1) บาท
This might be implying the full formula, but it's written strangely.
Perhaps they mean the total amount is something times (1.001^48 -1).
In the formula, FV = P * [(1+r)^n - 1] / r
For P=2500, r=0.001, n=48
First, calculate [(1.001^48 - 1) / 0.001]
Then multiply by 2500.
Option a has 2,502,500 (1.001^48 -1), which might mean 2,502,500 times (1.001^48 -1), but that doesn't make sense.
The way it's written: "2,502,500 (1.001^48 -1) บาท"
I think it's poorly formatted, but probably it means the amount is 2,502,500 multiplied by (1.001^48 -1), or perhaps it's the formula itself.
That doesn't align. Let's think differently.
Perhaps they are expressing the future value directly.
Another way: sometimes it's written as FV = P * S, where S is the sum factor.
But looking closely, option a is "2,502,500 (1.001^48 -1) บาท", which might be a mistake in transcription.
Perhaps it's meant to be the formula for FV.
Let's calculate the actual FV to compare.
First, calculate (1.001^48)
1.001^48 is approximately 1.04889 (using calculator or approximation).
More precisely, 1.001^48 = (1 + 0.001)^48 ≈ 1 + 48*0.001 + higher terms, but exactly it's about 1.048889.
Then, (1.001^48 - 1) = 1.048889 - 1 = 0.048889
Then, [ (1.001^48 -1) / 0.001 ] = 0.048889 / 0.001 = 48.889
Then, FV = 2500 * 48.889 ≈ 122,222.50 baht
That doesn't match any options directly. The options have 2,500,000 or 2,502,500, which are much larger.
Perhaps I have the wrong P. The deposit is 2,500 per month, but options have 2,500,000, which is 1,000 times larger, maybe a typo in the question.
In the question: "ฝากเงินจำนวน 2,500 บาท" which is 2,500 baht, but options have 2,502,500, which is two million five hundred thousand, no, 2,502,500 is two million five hundred two thousand five hundred.
In Thai, commas are used as thousand separators, so 2,500 is two thousand five hundred.
But options like 2,502,500 is two million five hundred two thousand five hundred.
That doesn't make sense for the calculation.
Perhaps the deposit is 2,500,000 baht? Let's double-check the question.
The question says: "ฝากเงินจำนวน 2,500 บาท" which is clearly 2,500 baht.
But the options have numbers like 2,502,500, which is much larger.
Perhaps it's a typo in the options, or maybe I need to look at the formula as is.
Another possibility: the option is "2,500 (1.001^48 -1) บาท", but in the message, it's "2,502,500", which might be a typo.
In the user's message: "a":"2,502,500 (1.001^48 -1) บาท"
Perhaps it's 2,500, and the 2,502,500 is a mistake.
That doesn't help.
Let's look back: in the first option, "2,502,500 (1.001^48 -1) บาท"
Perhaps it's meant to be the full expression.
Maybe it's for a different P.
Another thought: perhaps the 2,502,500 is not part of the formula; maybe it's the total.
This is confusing. Let's assume the options are meant to be the formula for FV.
For example, option a: 2,502,500 * (1.001^48 -1), but that would be huge.
Perhaps it's 2,500 * [ (1.001^48 -1) / r ], but the options don't have the / r.
Let's check option d: "2,500,000 (1,001^47 -1) บาท" which has 1,001, not 1.001, so that's wrong.
I think the correct formula is FV = P * [ (1+r)^n -1 ] / r, with P=2500, r=0.001, n=48.
So, the correct expression should be 2500 * [ (1.001^48 -1) / 0.001 ]
Looking at the options, none directly say that, but option a is "2,502,500 (1.001^48 -1) บาท", which might be a miswrite for 2500 * (1.001^48 -1), but that's not right.
Perhaps in some contexts, they write it as P * S, where S = [ (1+r)^n -1 ] / r, but here it's not.
Let's compare the options:
a: 2,502,500 (1.001^48 -1)
b: 2,500,000 (1.001^48 -1)
c: 2,502,500 (1.001^47 -1)
d: 2,500,000 (1,001^47 -1) -- 1,001 is 1001, which is wrong.
e: 2,502,500 (1.001^4 -1)
For the correct one, it should be for P=2500, n=48, r=0.001.
But none match exactly.
Perhaps the 2,502,500 is a typo, and it's meant to be 2,500.
Maybe the deposit is 2,500 per month, but the total is calculated as above.
Another idea: perhaps the option is "2,500 * (1.001^48 -1) / 0.001", but it's not written that way.
In the options, it's like "number (expression) บาท", so perhaps the number is P, and the expression is the factor.
For example, a: 2,502,500 times (1.001^48 -1)
But that doesn't make sense.
Perhaps it's a mistake, and the correct one is b: 2,500,000 (1.001^48 -1), but 2,500,000 is 2.5 million, which is not.
Let's calculate the actual number.
From earlier, FV = 2500 * [ (1.001^48 -1) / 0.001 ] ≈ 2500 * 48.889 = 122,222.50
None of the options match 122,222.
Unless the deposit is 2,500,000.
Perhaps in the question, "2,500" is "2,500,000" with a missing comma.
In Thai, sometimes numbers are written without commas, but in the message, it's "2,500".
In the user's message: "ฝากเงินจำนวน 2,500 บาท" which is 2,500.
But that doesn't match.
Perhaps it's 2,500 baht per month, and after 48 months, with interest, it's around 122k, but options are in millions, so maybe the question is for 2,500,000.
To make sense, let's assume the correct option is the one with the right n and r.
So, for 4 years, 48 months, so n=48.
Interest rate 1.2% per year, compounded monthly, so r=0.001 per month.
So, the expression should be P * [ (1.001^48 -1) / 0.001 ]
If P is 2,500, then it's 2,500 * that.
But options have 2,502,500, which is close to 2,500 if it's a typo.
Perhaps option a is meant to be 2,500 (1.001^48 -1), but it's written as 2,502,500.
This is messy. Perhaps the closest is a: 2,502,500 (1.001^48 -1), assuming 2,502,500 is a typo for 2,500.
Maybe in the context, the correct one is a, as it has the right exponent.
Another way: perhaps the formula in the option is for the sum, and 2,502,500 is not part of it.
I think the best is to go with the one that has the correct n=48 and r=0.001.
So, options a and b have (1.001^48 -1)
a has 2,502,500, b has 2,500,000.
If P is 2,500, then b has 2,500,000, which is 1,000 times larger.
Perhaps d has 2,500,000 and 1,001^47, which is wrong.
I think the most correct is a, assuming the number is wrong.
Perhaps the question has P=2,500, and the option is for that.
Let's check if 2,502,500 is a miswrite for 2,500.
In the first user's message, it was "5 apples", so no commas.
I need to pick a as the correct one, as it has the right formula.
So, I'll go with a.
Brief explanation: Adirek deposits 2,500 baht monthly for 48 months with monthly compounding at 0.1%, so the future value is 2,500 * [(1.001^48 - 1) / 0.001], which matches the form in option a.
Then, respond with {"correct_answer_key":"a"}
Adirek deposits 2,500 baht every month for 4 years (48 months) into an account with 1.2% annual interest compounded monthly, which equates to a monthly rate of 0.1% (or 0.001 in decimal). The future value of this annuity is calculated using the formula: FV = P × [(1 + r)^n - 1] / r, where P = 2,500, r = 0.001, and n = 48. This results in FV = 2,500 × [(1.001^48 - 1) / 0.001]. Among the options, choice A most closely aligns with this formula, though the number "2,502,500" may be a typo or misrepresentation for the correct calculation base.
{"correct_answer_key":"a"}
อดิเรกฝากเงิน 2,500 บาททุกเดือน และดอกเบี้ยทบต้นทุกเดือนในอัตรา 1.2% ต่อปี ซึ่งเท่ากับ 0.001 ต่อเดือน (1.2%/ปี / 12 เดือน/ปี) เมื่อใช้สูตรการคำนวณเงินฝากทบต้น โดยมีจำนวนงวดฝาก 48 เดือน (4 ปี) และดอกเบี้ยรายเดือน 0.001 (หรือ 0.1% ต่อเดือน) สูตรการคำนวณเงินฝากทบต้นคือ:
A = P x (((1 + r)^n - 1) / r)
โดยที่: A = จำนวนเงินรวมหลังจาก n งวด P = จำนวนเงินฝากต่อเดือน (2,500 บาท) r = ดอกเบี้ยรายเดือน (0.001 หรือ 0.1%) n = จำนวนงวด (48 เดือน)
เมื่อแทนค่าลงในสูตร จะได้:
A = 2,500 x (((1 + 0.001)^48 - 1) / 0.001) A = 2,500 x ((1.001^48 - 1))
ดังนั้นคำตอบที่ถูกต้องคือ:
{"correct_answer_key":"b"}
To solve this, we need to understand the concept of compound interest and the formula for the future value of a series of deposits.
First, let's identify the given information:
The annual interest rate is 1.2%, so the monthly interest rate is ( \frac{1.2%}{12} = 0.1% = 0.001 ) in decimal form.
The total number of periods (months) in 4 years is ( 4 \times 12 = 48 ) months.
The formula for the future value of a series of deposits is given by: [ FV = \sum_{i=0}^{n-1} P \times (1 + r)^i = P \times \frac{(1 + r)^n - 1}{r} ] where:
Substituting the given values: [ FV = 2500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} ] [ FV = 2,500,000 \times \frac{(1.001)^{48} - 1}{1} ] [ FV = 2,500,000 \times (1.001^{48} - 1) ]
Thus, the correct formula is represented by option B.
{"correct_answer_key":"b"}
To solve this, let's break it down:
The formula for the future value of a series (FV) with compound interest is:
[ FV = P \times \frac{(1 + r)^n - 1}{r} ]
Where:
However, the initial deposit is not explicitly mentioned as part of the series, but it seems there might be a slight confusion in interpreting the question directly. Typically, for a series of deposits (like this annuity), the formula applies directly.
Given the options and usual financial calculations:
The correct formula application seems to align with: [ FV = 2500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} ]
This matches closest with: [ 2,500 \times \frac{(1.001)^{48} - 1}{0.001} ] Or simply represented in terms of multiplication outside the formula as: [ 2,500,000 (1.001^{48} -1) / 1000 ] But accurately reflecting: [ 2,500,000 (1.001^{48} -1) ]
So, the closest and correct representation reflecting an accurate calculation process would be:
{"correct_answer_key":"b"}
To solve this problem, we need to calculate the future value of a series of monthly deposits with compound interest. The formula for the future value of a series of cash flows (like monthly deposits) is:
[ FV = PMT \times \left( \frac{(1 + r)^n - 1}{r} \right) ]
where:
Plugging in the values:
[ FV = 2500 \times \left( \frac{(1 + 0.001)^{48} - 1}{0.001} \right) ]
This corresponds to option A.
{"correct_answer_key":"a"}
คำอธิบายโดยย่อ:
ในกรณีนี้ อดิเรกฝากเงินทุกต้นเดือน (ทุกวันที่ 1) ซึ่งเทียบเท่ากับ “annuity due” (ฝากต้นงวด) อัตราดอกเบี้ย 1.2% ต่อปี คิดเป็น 0.1% (0.001) ต่อเดือน เมื่อคำนวณมูลค่าอนาคตของเงินฝากแบบ annuity due เป็นเวลา 48 เดือน (4 ปี) จะได้สูตร
Future Value = A × [( (1 + i)^n - 1 ) / i ] × (1 + i)
โดย A = 2,500 บาท, i = 0.001, n = 48
เมื่อนำมาจัดรูปให้ตรงกับตัวเลือกในโจทย์จะตรงกับ 2,502,500 × (1.001^48 - 1)
ตอบในรูป JSON:
{"correct_answer_key":"a"}
อัตราดอกเบี้ยต่อเดือน r = 1.2 % / 12 = 0.1 % = 0.001
อดิเรกฝากเงินต้นทุกต้นเดือน (annuity‑due) เป็นเวลา 4 ปี = 48 งวด
มูลค่าในสิ้นงวดที่ 48
FV = P [(1+r)^n – 1] ⁄ r × (1+r)
= 2 500 [(1.001^48 – 1) ⁄ 0.001] × 1.001
= 2 500 000 (1.001^48 – 1) × 1.001
= 2 502 500 (1.001^48 – 1)
ตรงกับตัวเลือก ก.
{"correct_answer_key":"a"}
ทุกวันที่ 1 ของเดือนหมายถึงฝากเงินต้นตอนต้นงวด ⇒ เป็นเงินงวดแบบ annuity due
ดอกเบี้ยต่อเดือน r = 1.2%/12 = 0.001
จำนวนงวด n = 4 ปี = 48 เดือน
มูลค่าในอนาคตของเงินงวดแบบ annuity due
FV = PMT × [(1+r)^n – 1]/r × (1+r)
= 2,500 × [(1.001)^48 – 1]/0.001 × 1.001
= 2,500,000 × 1.001 × [(1.001)^48 – 1]
= 2,502,500 × [(1.001)^48 – 1]
ตรงกับตัวเลือก ก. (a)
{"correct_answer_key":"a"}
เงินฝาก 2,500 บาทถูกนำเข้าบัญชีทุกต้นเดือน (annuity due) นาน 48 งวด
อัตราดอกเบี้ยต่อเดือน r = 1.2 %/12 = 0.001
มูลค่าในอนาคตของเงินฝากแบบต้นงวด (annuity due)
FV = P · (1+r) · [(1+r)ⁿ – 1]/r
= 2,500 · 1.001 · [(1.001)⁴⁸ – 1]/0.001
= 2,502,500 · (1.001⁴⁸ – 1)
ตรงกับตัวเลือก ก.
{"correct_answer_key":"a"}
The problem describes an annuity due where 2,500 baht is deposited on the first day of every month. With an annual interest rate of 1.2% compounded monthly, the monthly rate is 0.012/12 = 0.001 (or 0.1%). For an annuity due (deposits made at the beginning of each period), the future value after n deposits is given by:
Future Value = Payment × [( (1 + i)^n – 1 ) / i] × (1 + i)
Here, Payment = 2,500, i = 0.001, and n = 48 (since 4 years × 12 months). Plugging in, we get:
FV = 2,500 × [(1.001^48 – 1) / 0.001] × 1.001 = 2,502,500 × (1.001^48 – 1)
Thus, the correct answer is option A.
{"correct_answer_key": "a"}
การคำนวณเงินฝากในอนาคตเมื่อมีการฝากเงินรายเดือนคำนวณได้จากสูตรของเงินสะสมแบบ Annuity Due (ฝากเงินต้นเดือน) ดังนี้
FV = P × (1 + i) × ((1 + i)ⁿ – 1) / i
โดยที่
P = 2,500 บาท
i = 1.2% ต่อปี ÷ 12 = 0.1% ต่อเดือน = 0.001
n = จำนวนเดือนทั้งหมด = 4 × 12 = 48
แทนค่าในสูตรจะได้
FV = 2,500 × 1.001 × ((1.001)⁴⁸ – 1) / 0.001
= 2,502,500 × ((1.001)⁴⁸ – 1)
ดังนั้นคำตอบที่ตรงกับสูตรคือข้อ (a)
{"correct_answer_key": "a"}
คำอธิบาย: อดิเรกฝากเงินเดือนละ 2,500 บาท เมื่อฝากทุกวันที่ 1 ของเดือน (แบบจ่ายตอนต้น) เมื่อคิดดอกเบี้ยทบต้นรายเดือน (อัตรารายเดือน = 1.2%/12 = 0.1% หรือ 0.001) ในระยะเวลา 4 ปี จะมีทั้งหมด 48 งวด การคำนวณเงินในบัญชีสำหรับเงินฝากแบบจ่ายตอนต้น (annuity due) คือ
FV = P × (1 + i) × ((1 + i)ⁿ – 1) / i
โดยแทนค่า P = 2,500, i = 0.001 และ n = 48 เราจะได้
FV = 2,500 × 1.001 × ((1.001⁴⁸ – 1) / 0.001) = 2,502,500 × (1.001⁴⁸ – 1)
ซึ่งตรงกับตัวเลือก a
{"correct_answer_key": "a"}
นี่เป็นกรณีเงินฝากรายเดือนต้นงวด (annuity due) อัตราดอกเบี้ยต่อเดือน = 1.2%/12 = 0.001 จำนวนงวด = 4×12 = 48 วิธีคำนวณมูลค่าครบกำหนดคือ
FV = 2,500 × ((1.001^48 − 1) / 0.001) × 1.001
ซึ่งเท่ากับ 2,502,500 × (1.001^48 − 1) จึงตรงกับข้อ a
{"correct_answer_key":"a"}
อัตราดอกเบี้ยเดือนละ 1.2%/12=0.001, ฝากทุกต้นเดือนเป็น annuity due 48 งวด
FV = 2500·[(1.001^48−1)/0.001]·1.001 = 2,502,500·(1.001^48−1)
{"correct_answer_key":"a"}
ฝากเงินทุกวันที่ 1 ของเดือน เป็นเงินงวดล่วงหน้า (annuity due) จำนวน n=4×12=48 ครั้ง อัตราดอกเบี้ย 1.2% ต่อปี หรือ i=0.001 ต่อเดือน จึงใช้สูตร
A = P·[(1+i)^n − 1]/i · (1+i) = 2,500·[(1.001^48−1)/0.001]·1.001 = 2,502,500·(1.001^48 − 1)
{"correct_answer_key":"a"}
To solve this problem, we need to calculate the future value of a series of monthly deposits with compound interest. The formula for the future value of a series of regular deposits (an annuity) is:
[ FV = P \times \frac{(1 + r)^n - 1}{r} ]
Where:
Given:
Plugging these values into the formula:
[ FV = 2,500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} ]
This simplifies to:
[ FV = 2,500 \times \frac{(1.001^{48} - 1)}{0.001} ]
The correct expression for the future value is:
[ 2,500 \times \frac{(1.001^{48} - 1)}{0.001} ]
This matches option A, which is:
[ 2,502,500 \times (1.001^{48} - 1) ]
The factor of 2,502,500 is derived from multiplying 2,500 by 1,001 (since ( \frac{1}{0.001} = 1,000 ) and ( 2,500 \times 1,000 = 2,500,000 ), and the extra 500 comes from the multiplication by 1.001).
Thus, the correct answer is:
{"correct_answer_key":"a"}
To solve this problem, we need to calculate the future value of a series of monthly deposits into a savings account that earns compound interest. This is a future value of an annuity problem, where deposits are made at the beginning of each month, and interest is compounded monthly.
The formula for the future value of an annuity (with monthly compounding) is: $$ FV = PMT \times \frac{(1 + i)^n - 1}{i} $$ Where:
Substitute the values into the formula: $$ FV = 2,500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} $$
Simplify the terms:
Multiply by the monthly deposit ($ PMT = 2,500 $) to get the final future value.
After performing the calculation, the correct expression for the future value matches option A: $$ FV = 2,500 \times \frac{(1.001^{48} - 1)}{0.001} = 2,502,500 \times (1.001^{48} - 1) $$
{"correct_answer_key":"a"}
Okay, let's tackle this problem step by step. The question is in Thai, so I need to make sure I understand it correctly. Let me translate the key points:
"Every 1st of the month, Adirek deposits 2,500 baht into a bank account that compounds interest monthly at a rate of 1.2% per year. When 4 years have passed, how much will Adirek's total deposit in this account be?"
Hmm, so it's about compound interest with monthly deposits. The key here is that it's an annuity problem, specifically a monthly compounded annuity. The formula for the future value of a series of monthly deposits is needed here.
First, let's recall the formula for the future value of an ordinary annuity (since deposits are made at the beginning of each month, actually, wait, the problem says "every 1st of the month," which is the start of the month, so it might be an annuity due. Wait, but sometimes in formulas, ordinary annuity is end of period. Need to confirm that.
Wait, the problem says "ฝากเงินจำนวน 2,500 บาทเข้าบัญชีธนาคารที่คิดดอกเบี้ยเงินฝากทบต้นทุกเดือน" which translates to depositing on the 1st of each month, so that's the start of the month. So this is an annuity due (payments at the beginning of the period), which compounds monthly. The formula for annuity due is FV = PMT * [( (1 + r)^n - 1 ) / r ] * (1 + r).
Alternatively, if it's treated as an ordinary annuity (end of month), the formula is FV = PMT * [ ( (1 + r)^n -1 ) / r ]. But since the deposit is on the 1st, it's annuity due, so we need to adjust for that.
But let me check the given options to see if they account for that. Let's see the options:
Options a and b have 2,502,500 and 2,500,000 multiplied by (1.001^48 -1). Wait, 2,500 is the monthly deposit, so where does 2,502,500 come from? Wait, maybe there's a miscalculation here. Let me think again.
Wait, the monthly deposit is 2,500 baht. The options have coefficients like 2,502,500 or 2,500,000. That seems like they might have multiplied 2,500 by 1,001? Wait, 2,500 * 1001 would be 2,502,500. Hmm, perhaps there's a typo or misunderstanding here. Alternatively, maybe the options are written with the formula components.
Wait, let's parse the options again carefully:
Option a: 2,502,500 (1.001^48 -1)
Option b: 2,500,000 (1.001^48 -1)
Option c: 2,502,500 (1.001^47 -1)
Option d: 2,500,000 (1,001^47 -1) – note the comma here might be a decimal, but written as 1,001 could be 1.001?
Option e: 2,502,500 (1.001^4 -1)
Hmm, the exponent in the first options is 48, which is 4 years * 12 months, so that makes sense. The exponent 47 would be one less, perhaps if it's an ordinary annuity instead of annuity due?
Wait, let's get back to the problem. The key steps are:
Determine the monthly interest rate. The annual rate is 1.2%, so monthly is 1.2% / 12 = 0.1% per month. So 0.001 in decimal. So the rate r is 0.001.
The number of periods n is 4 years * 12 = 48 months.
The payment PMT is 2,500 baht each month.
Now, the future value of an ordinary annuity (end of period payments) is FV = PMT * [ ( (1 + r)^n -1 ) / r ]
But since the deposits are made at the beginning of each month (annuity due), the formula is FV = PMT * [ ( (1 + r)^n -1 ) / r ] * (1 + r)
Alternatively, the formula can be written as FV = PMT * [ ( (1 + r)^n -1 ) / r ] * (1 + r)
So let's compute that.
First, let's compute the ordinary annuity part:
[ (1.001)^48 -1 ] / 0.001
Then multiply by PMT (2500) and then by (1.001) for the annuity due.
So total FV = 2500 * [ (1.001^48 -1)/0.001 ] * 1.001
Alternatively, that can be written as 2500 * 1.001 * [ (1.001^48 -1)/0.001 ]
But let's see the options. Let's see if any of them match this structure.
Looking at the options, the coefficients in front of the (1.001^n -1) term are either 2,502,500 or 2,500,000. Let's see:
If we factor out the 2500, then:
The term [ (1.001^48 -1)/0.001 ] * 1.001 multiplied by 2500 would be:
2500 * 1.001 * [ (1.001^48 -1)/0.001 ]
But 2500 * 1.001 = 2502.5, so that would be 2502.5 * [ (1.001^48 -1)/0.001 ]
Wait, but the options have 2,502,500 which is 2502.5 * 1000, so perhaps they have multiplied by 1000? Let me see:
Wait, let's see the formula again. Let me re-express the formula step by step.
The standard formula for annuity due is:
FV = PMT * [ ((1 + r)^n -1)/r ] * (1 + r)
So substituting the values:
PMT = 2500
r = 0.001
n =48
So FV = 2500 * [ (1.001^48 -1)/0.001 ] * 1.001
Let me compute the constants:
First, compute [ (1.001^48 -1)/0.001 ]
Let me denote that term as A = (1.001^48 -1)/0.001
Then multiply by 2500 and 1.001:
FV = 2500 * 1.001 * A
But A is (1.001^48 -1)/0.001, so:
FV = 2500 * 1.001 * (1.001^48 -1)/0.001
Simplify the constants:
2500 * 1.001 / 0.001 = 2500 * (1.001 / 0.001) = 2500 * 1001
Because 1.001 divided by 0.001 is 1001 (since 1.001 /0.001 = 1001).
Therefore, FV = 2500 * 1001 * (1.001^48 -1 )
Wait, that's 2500 * 1001 = 2,502,500. So the entire expression becomes:
FV = 2,502,500 * (1.001^48 -1 )
Looking at the options, that's exactly option a: "2,502,500 (1.001^48 -1) บาท"
Wait, but let me check again. Because in the annuity due formula, the (1 + r) is multiplied at the end. So the steps are correct?
Yes, because the annuity due formula is ordinary annuity multiplied by (1 + r). The ordinary annuity formula is PMT * [ ( (1 + r)^n -1 ) / r ]
So when you multiply by (1 + r), you get PMT * [ ( (1 + r)^n -1 ) / r ] * (1 + r )
Which can be written as PMT*(1 + r)/r * [ (1 + r)^n -1 ]
Wait, but in the calculation above, when I broke it down, the 2500 *1.001 /0.001 is indeed 2500 * (1.001 /0.001) = 2500 * 1001, so that term is correct. Then multiplied by (1.001^48 -1). So the formula matches option a.
But let me check the other options to be sure.
Option b is 2,500,000 multiplied by the same term. The difference is that 2,500,000 is 2500 * 1000, so they might have forgotten to multiply by the extra 1.001, hence missing the annuity due adjustment. So option b would be the ordinary annuity formula, not considering the beginning of the month.
Option c has 2,502,500 but with exponent 47. That might be if they considered n-1, but why?
Alternatively, maybe the exponent is 47 because the first deposit is made at time 0, so it compounds for 48 months, but the last deposit compounds for 1 month. Wait, but the formula already accounts for all periods. Hmm, perhaps a miscalculation in the exponent?
Alternatively, maybe the question is actually an ordinary annuity (end of month), so the exponent would be 48, but the coefficient would be 2500*(1/0.001) = 2,500,000, so option b would be the ordinary annuity. But since the problem states the deposit is on the 1st of each month, which is the start, so annuity due is correct, so option a is correct.
Wait, but let me check the exponent again. The exponent in the formula is n, which is 48. So the term (1.001)^48 is correct. So option a has that exponent. So the correct answer should be a?
Wait, but let me think again. Let me verify with an example.
Suppose only 1 month: deposit 2500 on day 1. After 1 month, the amount is 2500*(1.001). So the FV would be 25001.001. According to the formula in option a, when n=1, it would be 2502500(1.001^1 -1) = 2502500*(0.001) = 2502.5, but the actual FV is 2500*1.001 = 2502.5. So that matches. So the formula in option a works for n=1.
If n=2, then the first deposit earns two months' interest, the second earns one month. So total FV = 2500*(1.001)^2 + 2500*(1.001).
Using the formula in option a: 2502500*(1.001^2 -1). Let's compute that:
(1.001^2 -1) = (1.002001 -1) = 0.002001
Multiply by 2502500: 2502500 *0.002001 ≈ 2502500 0.002 = 5005, plus 25025000.000001=2.5025, so total ≈5007.5025
But the actual FV is 2500*(1.001)^2 +2500*(1.001) =2500*(1.001)(1.001 +1) =25001.001(2.001)
Compute 25001.001=2502.5, then 2.001: 2502.52=5005, plus 2502.50.001=2.5025 → total 5007.5025. So matches. So the formula in option a is correct for n=2.
Therefore, the formula in option a is correct. So the answer should be a.
Wait, but let me check the other options again. Option c has exponent 47. Maybe someone thought that the first deposit doesn't get the extra month? But no, in annuity due, each deposit is at the start, so the first deposit gets n months, the second n-1, etc. So the total is sum_{k=1 to n} PMT*(1+r)^k = PMT*(1+r)*[ ( (1+r)^n -1 ) / r ]
Which is exactly the formula in option a. So yes, option a is correct.
Therefore, the correct answer is option a.
Adirek deposits 2,500 baht monthly on the 1st of each month (annuity due) into an account with a 1.2% annual interest rate compounded monthly. The monthly rate is 0.1% (1.2% / 12). Over 4 years (48 months), the future value formula for an annuity due is:
FV = PMT × [(1 + r)^n - 1]/r × (1 + r).
Substituting values:
This simplifies to:
2,500 × 1.001 × [(1.001^48 - 1)/0.001],
which equals 2,502,500 × (1.001^48 - 1).
The correct answer is a, as it matches this formula.
{"correct_answer_key":"a"}
To calculate the total amount of money Adirek will have in his account after 4 years, we need to consider both the monthly deposits and the interest.
Adirek deposits 2,500 baht every month, so in 4 years (48 months), he will deposit a total of 2,500 * 48 = 120,000 baht.
The interest rate is 1.2% per year, which is equivalent to 0.0012 per month. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, we have monthly deposits, so we need to use the formula for compound interest with monthly deposits: A = PMT * (((1 + r/n)^(nt) - 1) / (r/n)), where PMT is the monthly deposit.
Plugging in the values, we get A = 2,500 * (((1 + 0.0012)^(48) - 1) / 0.0012).
This corresponds to option A: 2,502,500 (1.001^48 -1) บาท.
{"correct_answer_key":"a"}
Alright! Let's tackle this problem step by step. The question is about calculating the future value of a series of monthly deposits with compound interest.
First, I need to understand the details given:
Since the interest is compounded monthly, the annual rate needs to be converted to a monthly rate. The annual rate is 1.2%, so the monthly rate would be 1.2% divided by 12, which is 0.1% per month, or 0.001 in decimal form.
Next, we need to determine the number of periods. Over 4 years, there are 48 months (since 4 years * 12 months = 48 months).
This situation describes an ordinary annuity because deposits are made at the end of each period (in this case, at the beginning of each month, but since it's compounded monthly, it's treated as an ordinary annuity).
The formula for the future value of an ordinary annuity is: [ FV = PMT \times \frac{(1 + r)^n - 1}{r} ] Where:
Plugging in the numbers: [ FV = 2500 \times \frac{(1 + 0.001)^{48} - 1}{0.001} ]
Looking at the options provided, option A is "2,502,500 (1.001^48 -1) บาท". This matches the structure of our formula if we factor out the 2500. However, 2500 multiplied by 1000 is 2,500,000, not 2,502,500. Therefore, option A seems incorrect due to the discrepancy in the multiplier.
Option B is "2,500,000 (1.001^48 -1) บาท". This aligns perfectly with our calculation because 2500 * 1000 = 2,500,000, and the exponent and subtraction match the formula.
Options C, D, and E either use the wrong exponent (47 instead of 48) or incorrect multipliers, making them incorrect.
Thus, the correct answer should be option B.
{"correct_answer_key":"b"}