This problem involves a future value of an annuity calculation where regular monthly payments are made, and interest is compounded monthly. Let's go through it step by step:

Given Information:

• Monthly deposit (PMT): $100
• Interest rate (annual): 7% or 0.07
• Time period: 15 years
• Compounding frequency: Monthly (12 times a year)

We'll use the formula for the future value of an ordinary annuity:

$FV = PMT \times \frac{(1 + r/n)^{nt} - 1}{r/n}$

Where:

• $FV$ = future value of the account
• $PMT$ = monthly deposit ($100)
• $r$ = annual interest rate (7% or 0.07)
• $n$ = number of compounding periods per year (12)
• $t$ = time in years (15)

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

We'll calculate this value using the formula above.

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

To calculate this, we simply multiply the monthly deposit by the total number of months: $\text{Total contributions} = PMT \times (n \times t)$

Part c) How much total interest will you earn?

The total interest earned is the difference between the future value and the total contributions: $\text{Total interest} = FV - \text{Total contributions}$

Now, let's compute the values.### Results:

a) The amount in the account after 15 years will be $31,696.23.

b) The total money you will have put into the account is $18,000.

c) The total interest earned will be $13,696.23.

Would you like more details or have any questions about the process?

Here are 5 related questions for further exploration:

1. How would the final amount change if the interest rate were 5% instead of 7%?
2. What happens to the future value if the deposits were made at the beginning of each month?
3. How much would you have after 10 years instead of 15 years?
4. How would the total interest change if you increased the monthly deposit to $200?
5. What if the interest compounded quarterly instead of monthly?

Tip: When saving for the long term, small differences in interest rates and compounding frequency can significantly impact the total interest earned.