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).