You deposit $500 each month into an account earning 4% 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 solve this step by step.

### Given:
- Monthly deposit: $ P = 500 $
- Annual interest rate: $ r = 4\% = 0.04 $
- Interest compounded monthly: $ n = 12 $ times per year
- Time: $ t = 15 $ years

We'll use the formula for the future value of a series of monthly payments compounded monthly:

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

Where:
- $ A $ = total amount in the account
- $ P $ = monthly payment
- $ r $ = annual interest rate (as a decimal)
- $ n $ = number of times the interest is compounded per year (monthly = 12)
- $ t $ = number of years

### Part a) Calculate the amount in the account after 15 years:

\[
A = 500 \times \frac{(1 + \frac{0.04}{12})^{12 \times 15} - 1}{\frac{0.04}{12}}
\]

Let me calculate that.a) The amount in the account after 15 years will be approximately **$123,045.24**.

### Part b) Calculate the total money deposited:

You deposit $500 each month for 15 years. The total amount deposited is:

\[
\text{Total Deposits} = P \times n \times t = 500 \times 12 \times 15
\]

Let me calculate that.b) The total money deposited into the account over 15 years is **$90,000**.

### Part c) Calculate the total interest earned:

The total interest is the difference between the future value and the total deposits:

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

Let me calculate that.c) The total interest earned over 15 years is approximately **$33,045.24**.

---

Would you like further details or explanations? Here are some related questions for practice:

1. What would happen if the interest rate was 5% instead of 4%?
2. How much would you have if you deposited $400 monthly instead of $500?
3. What is the balance after 10 years instead of 15 years?
4. How does compounding quarterly change the final balance compared to monthly?
5. What is the formula for continuous compounding, and how would it affect your result?

**Tip**: Small increases in the interest rate can lead to significant growth due to compounding over long periods.

You deposit $500 each month into an account earning 4% 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?

Learn how to calculate the future value of depositing $500 each month into an account with 4% interest compounded monthly over 15 years. This guide explains how much money you'll accumulate, how much you've deposited, and the total interest earned. Suitable for Grades 10-12 students or anyone studying compound interest.

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