FV of Annuity

To find the future value (FV) of an annuity, we can use the formula:

FV = a / {(1 + i) ^ n - 1}

Given:
- Principal amount (A) = 100
- Number of periods (n) = 10
- Interest rate (i) = 5%

Step 1: Determine the periodic payment (a)
In this case, the periodic payment is not given explicitly. However, since the question mentions that it is an annuity, we can assume that the periodic payment is the same for each period. Therefore, we can calculate the periodic payment (a) by dividing the principal amount (A) by the number of periods (n).

a = A / n
a = 100 / 10
a = 10

So, the periodic payment (a) is 10.

Step 2: Calculate the future value (FV)
Now that we have the periodic payment (a), we can substitute the values into the formula to calculate the future value (FV) of the annuity.

FV = a / {(1 + i) ^ n - 1}
FV = 10 / {(1 + 0.05) ^ 10 - 1}

Calculating the denominator first:

(1 + 0.05) ^ 10 = 1.628895

Substituting the values back into the formula:

FV = 10 / (1.628895 - 1)
FV = 10 / 0.628895
FV ≈ 15.92

So, the future value (FV) of the annuity is approximately 15.92.

Explanation:
The future value of an annuity is the total value of all the periodic payments made over a specific time period, considering the interest earned on those payments. The formula for calculating the future value of an annuity takes into account the periodic payment (a), the interest rate (i), and the number of periods (n).

In this case, we were given the principal amount (A), which can be considered as the present value of the annuity. We then calculated the periodic payment (a) by dividing the principal amount by the number of periods. Finally, we substituted the values into the formula to calculate the future value (FV) of the annuity.

It is important to note that the future value of an annuity assumes that the periodic payments are made at the end of each period and that the interest is compounded annually. Additionally, the formula assumes that the interest rate remains constant throughout the annuity's duration.