Suppose you invest $120 a month for 4 years into an account earning 6% compounded monthly. After 4 years, you leave the money, without making additional deposits, in the account for another 29 years. How much will you have in the end?

To solve this problem, we can break it into two parts:

### Part 1: Regular Investment for 4 Years
You are investing $120 every month into an account earning 6% interest compounded monthly. The formula for the future value of a series of monthly investments (an annuity) is given by:

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

Where:
- $ A $ = future value of the annuity (the account balance after the 4 years of deposits),
- $ P $ = monthly investment ($120),
- $ r $ = monthly interest rate ($ \frac{6\%}{12} = 0.005 $),
- $ n $ = total number of deposits ($ 4 \times 12 = 48 $).

### Part 2: Leaving the Money for 29 Years
After 4 years, you stop making monthly deposits, and the balance from Part 1 grows for 29 more years at the same interest rate, compounded monthly. The formula for compound interest is:

\[
A_{\text{final}} = A_{\text{initial}} \times (1 + r)^{n}
\]

Where:
- $ A_{\text{final}} $ = account balance after the 29 years,
- $ A_{\text{initial}} $ = account balance from Part 1,
- $ r $ = monthly interest rate (0.005),
- $ n $ = total number of months in 29 years ($ 29 \times 12 = 348 $).

Let's compute the final amount.After 4 years of monthly investments and leaving the money to grow for an additional 29 years, you will have approximately **$36,825.67** in the account.

Would you like a detailed breakdown of the steps, or do you have any other questions?

Here are five related questions to explore:
1. What happens if the interest rate was compounded quarterly instead of monthly?
2. How much would the total amount be if the investment period was longer, say 6 years, instead of 4?
3. How much would you need to invest each month to reach $50,000 after the same time period?
4. What would be the impact of different annual interest rates (e.g., 5% or 7%) on the final amount?
5. How does the total amount change if the investment is compounded daily instead of monthly?

**Tip**: Compounding frequency has a significant impact on the growth of an investment, especially over long periods.

Discover how a $120 monthly investment compounded at 6% interest for 4 years can grow significantly over 29 more years without additional deposits. This example illustrates the use of annuity and compound interest formulas. Suitable for Grades 10-12 students.

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