Question

What is the future value of an IRA if you deposit $1500 annually with a 9% interest rate that compounds annually from age 25 to 60?

Answer 1

To calculate the future value of an IRA with annual deposits, we use the future value of an annuity formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( FV \) = future value of the annuity
- \( P \) = annual payment (deposit)
- \( r \) = annual interest rate (as a decimal)
- \( n \) = number of deposits (years)

In this case:
- \( P = 1500 \) (the annual deposit)
- \( r = 0.09 \) (9% interest rate)
- \( n = 60 - 25 = 35 \) (the number of years from age 25 to 60)

Now, we can plug in the values:

\[
FV = 1500 \times \frac{(1 + 0.09)^{35} - 1}{0.09}
\]

Calculating \( (1 + 0.09)^{35} \):

\[
(1.09)^{35} \approx 14.2397
\]

Now substitute this back into the formula:

\[
FV = 1500 \times \frac{14.2397 - 1}{0.09}
\]

\[
FV = 1500 \times \frac{13.2397}{0.09}
\]

Calculating \( \frac{13.2397}{0.09} \):

\[
\frac{13.2397}{0.09} \approx 147.108
\]

Now, multiply by 1500:

\[
FV \approx 1500 \times 147.108 \approx 220662
\]

So the future value of the IRA at age 60, after making annual deposits of $1500 with a 9% interest rate compounded annually, will be approximately **$220,662**.