You deposit $400 each month into an account earning 3% interest compounded monthly.

a) How much will you have in the account in 15 years?

$

b) How much total money will you put into the account?

$

c) How much total interest will you earn?

Let's break down the problem step by step.

### Part a) Amount in the Account After 15 Years

This is a future value problem of an annuity, where you're making regular monthly deposits and interest is compounded monthly. The formula for the future value of an annuity is:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the monthly deposit ($400).
- $ r $ is the monthly interest rate.
- $ n $ is the total number of deposits.

Given:
- Annual interest rate = 3%, so monthly interest rate $ r = \frac{3\%}{12} = \frac{0.03}{12} = 0.0025 $.
- Number of years = 15, so the total number of deposits $ n = 15 \times 12 = 180 $.

Now, let's calculate:

\[
FV = 400 \times \left(\frac{(1 + 0.0025)^{180} - 1}{0.0025}\right)
\]

### Part b) Total Money Deposited

This is simply the total amount of money you have deposited over the 15 years:

\[
\text{Total Deposits} = P \times n = 400 \times 180
\]

### Part c) Total Interest Earned

The total interest earned is the difference between the future value of the account and the total amount deposited:

\[
\text{Total Interest} = FV - \text{Total Deposits}
\]

I'll calculate each of these.Here are the results:

a) **Amount in the account after 15 years**: $90,789.08

b) **Total money deposited**: $72,000

c) **Total interest earned**: $18,789.08

Would you like more details or have any questions? Here are some related questions to explore:

1. How would the future value change if the interest rate increased to 4%?
2. What if you made an initial lump sum deposit along with the monthly deposits?
3. How much interest would you earn if you only deposited $200 per month?
4. What would be the future value after 10 years instead of 15?
5. How does compounding frequency (monthly vs. quarterly) affect the future value?

**Tip:** Compounding more frequently (e.g., monthly) generally leads to higher future values compared to less frequent compounding (e.g., annually).

Learn how to calculate the future value of monthly deposits with 3% interest compounded monthly over 15 years. Discover the total amount accumulated, total deposits made, and total interest earned. Suitable for high school students learning compound interest calculations.

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