In order to accumulate enough money for a down payment on a house, a couple deposits $639 per month into an account paying 6% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 3 years?

To solve this problem, we can use the formula for the future value of an ordinary annuity, which is applicable when regular payments are made at the end of each period. The formula is:

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

Where:
- $ FV $ is the future value of the account.
- $ P $ is the regular payment ($639 per month).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (number of months).

### Step 1: Identify the values
- Monthly payment ($ P $) = 639
- Annual interest rate = 6%, so the monthly interest rate ($ r $) = $\frac{6}{12} = 0.5\%$ or 0.005.
- Number of payments ($ n $) = 3 years $\times$ 12 months/year = 36 months.

### Step 2: Plug the values into the formula

\[
FV = 639 \times \frac{{(1 + 0.005)^{36} - 1}}{0.005}
\]

Now, let's calculate the future value.The future value of the account after 3 years, with monthly payments of $639 at 6% interest compounded monthly, will be approximately **$25,135.77**.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What happens to the future value if the interest rate increases?
2. How would the total amount change if payments were made at the beginning of each period?
3. What is the impact of making extra payments on the future value of the account?
4. How much of the future value comes from interest versus principal payments?
5. How would the calculation change if the compounding frequency were quarterly instead of monthly?

**Tip:** Compounding interest frequently can significantly increase your investment growth over time!

Learn how to calculate the future value of monthly deposits of $639 over 3 years at 6% interest compounded monthly. This example uses the future value of an ordinary annuity formula and covers key financial concepts. Suitable for students in Grades 10-12.

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