Suppose you want to have $600,000 for retirement in 35 years. Your account earns 5% interest.

a) How much would you need to deposit in the account each month?

$

b) How much interest will you earn?

$
Question

We can solve this retirement savings problem using the **Future Value of an Annuity formula**, which calculates the amount of regular monthly contributions needed to reach a target future sum with compound interest.

### a) Calculating the Monthly Deposit
The future value of an annuity formula is:

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

Where:
- $FV$ is the future value, in this case, $600,000.
- $P$ is the monthly deposit.
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of deposits (number of years times 12).

We are given:
- $FV = 600,000$
- Annual interest rate = 5%, so the monthly interest rate $r = \frac{5\%}{12} = 0.004167$
- Time = 35 years, so the number of deposits $n = 35 \times 12 = 420$

We need to solve for $P$, the monthly deposit.

Let me calculate it.

Suppose you want to have $600,000 for retirement in 35 years. Your account earns 5% interest.

a) How much would you need to deposit in the account each month?

b) How much interest will you earn?

Learn how to calculate the required monthly deposits to accumulate $600,000 for retirement over 35 years with a 5% interest rate. This problem involves the Future Value of an Annuity formula and covers concepts in compound interest and algebra. Suitable for high school students in Grades 10-12.

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