CA Foundation Exam > CA Foundation Questions > A=100, n=10, i=5 % find the FV of annuity?
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A=100, n=10, i=5 % find the FV of annuity?
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A=100, n=10, i=5 % find the FV of annuity?
**Future Value of Annuity**
The future value of an annuity is the total value of a series of equal cash flows received or paid at regular intervals over a specified period of time. It represents the accumulated value of these cash flows at a future date, taking into account the interest earned on the invested amount.
To calculate the future value of an annuity, we need to know the following variables:
- A: The amount of each annuity payment. In this case, A = 100.
- n: The number of periods or payments. Here, n = 10.
- i: The interest rate per period. Given i = 5%.
Now, let's calculate the future value of the annuity using the following formula:
FV = A * ((1 + i)^n - 1) / i
**Step 1: Calculate (1 + i)^n**
(1 + i)^n = (1 + 0.05)^10
= 1.05^10
= 1.628895
**Step 2: Calculate the numerator**
Numerator = (1 + i)^n - 1
= 1.628895 - 1
= 0.628895
**Step 3: Calculate FV**
FV = A * (numerator / i)
= 100 * (0.628895 / 0.05)
= 100 * 12.5779
= 1257.79
Therefore, the future value of the annuity is $1257.79.
**Explanation:**
The future value of an annuity can be understood as the total amount that will be accumulated at the end of the annuity period. It takes into account the periodic cash flows, the number of periods, and the interest rate.
In this case, the annuity payment is $100, and there are 10 periods. The interest rate per period is 5%. By plugging these values into the formula, we can calculate the future value.
In Step 1, we calculate (1 + i)^n, which represents the growth factor of the annuity. Here, it is approximately 1.628895.
In Step 2, we calculate the numerator, which is the difference between (1 + i)^n and 1. In this case, it is approximately 0.628895.
Finally, in Step 3, we multiply the annuity payment by the numerator divided by the interest rate. This gives us the future value of the annuity, which is approximately $1257.79.
The future value of an annuity is an important concept in finance as it helps individuals and businesses plan for their future financial needs. By understanding the future value, one can make informed decisions regarding investments, savings, and retirement planning.
The future value of an annuity is the total value of a series of equal cash flows received or paid at regular intervals over a specified period of time. It represents the accumulated value of these cash flows at a future date, taking into account the interest earned on the invested amount.
To calculate the future value of an annuity, we need to know the following variables:
- A: The amount of each annuity payment. In this case, A = 100.
- n: The number of periods or payments. Here, n = 10.
- i: The interest rate per period. Given i = 5%.
Now, let's calculate the future value of the annuity using the following formula:
FV = A * ((1 + i)^n - 1) / i
**Step 1: Calculate (1 + i)^n**
(1 + i)^n = (1 + 0.05)^10
= 1.05^10
= 1.628895
**Step 2: Calculate the numerator**
Numerator = (1 + i)^n - 1
= 1.628895 - 1
= 0.628895
**Step 3: Calculate FV**
FV = A * (numerator / i)
= 100 * (0.628895 / 0.05)
= 100 * 12.5779
= 1257.79
Therefore, the future value of the annuity is $1257.79.
**Explanation:**
The future value of an annuity can be understood as the total amount that will be accumulated at the end of the annuity period. It takes into account the periodic cash flows, the number of periods, and the interest rate.
In this case, the annuity payment is $100, and there are 10 periods. The interest rate per period is 5%. By plugging these values into the formula, we can calculate the future value.
In Step 1, we calculate (1 + i)^n, which represents the growth factor of the annuity. Here, it is approximately 1.628895.
In Step 2, we calculate the numerator, which is the difference between (1 + i)^n and 1. In this case, it is approximately 0.628895.
Finally, in Step 3, we multiply the annuity payment by the numerator divided by the interest rate. This gives us the future value of the annuity, which is approximately $1257.79.
The future value of an annuity is an important concept in finance as it helps individuals and businesses plan for their future financial needs. By understanding the future value, one can make informed decisions regarding investments, savings, and retirement planning.
Community Answer
A=100, n=10, i=5 % find the FV of annuity?
Calculator trick:- 5÷100+1×= 9 times -1÷5×100×100=1257.79
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A=100, n=10, i=5 % find the FV of annuity? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A=100, n=10, i=5 % find the FV of annuity? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A=100, n=10, i=5 % find the FV of annuity?.
A=100, n=10, i=5 % find the FV of annuity? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A=100, n=10, i=5 % find the FV of annuity? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A=100, n=10, i=5 % find the FV of annuity?.
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