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It looks like you're working on a question related to annuities, specifically savings annuities with monthly contributions and compounded interest. Let's break it down.

The problem is asking:

1. You deposit $200 each month into an account earning 6% interest compounded monthly.
2. You need to calculate:
   - (a) How much you will have in the account in 15 years.
   - (b) How much total money you will put into the account.
   - (c) How much total interest you will earn.

### Step-by-Step Solution:

To solve for (a), we will use the formula for the future value of an annuity (since payments are made regularly):

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

Where:
- $FV$ = future value (what we are solving for)
- $P$ = monthly payment = 200
- $r$ = annual interest rate = 6% or 0.06
- $n$ = number of times interest is compounded per year = 12 (monthly)
- $t$ = number of years = 15

#### For (a): 
\[
FV = 200 \times \frac{{(1 + 0.06/12)^{12 \times 15} - 1}}{{0.06/12}}
\]

\[
FV = 200 \times \frac{{(1 + 0.005)^{180} - 1}}{{0.005}}
\]
\[
FV = 200 \times \frac{{(1.005)^{180} - 1}}{{0.005}}
\]
Using a calculator, $(1.005)^{180} \approx 2.4596$.

\[
FV = 200 \times \frac{{2.4596 - 1}}{{0.005}} = 200 \times 291.921 = 58,384.20
\]

So, the amount in the account after 15 years is approximately **$58,384.20**.

#### For (b): 
The total money you put into the account is simply the monthly deposit multiplied by the total number of months:

\[
Total\;Deposits = 200 \times 12 \times 15 = 200 \times 180 = 36,000
\]

So, you will put in a total of **$36,000**.

#### For (c): 
The total interest earned is the future value minus the total deposits:

\[
Interest = 58,384.20 - 36,000 = 22,384.20
\]

Thus, the total interest earned is approximately **$22,384.20**.

Let me know if you would like further details or have any specific questions! Here are some related questions to consider:

1. How would the total future value change if the interest rate were 8%

You deposit $200 each month into an account earning 6% interest compounded monthly. How much will you have in the account in 15 years? How much total money will you put into the account? How much total interest will you earn?

Learn how to calculate the future value of a savings annuity with monthly deposits of $200, a 6% interest rate compounded monthly over 15 years. This includes finding the total amount in the account, total deposits made, and total interest earned. Suitable for high school and introductory college students.

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