You deposit $350 each month into an account earning 8% interest compounded monthly.

a) How much will you have in the account in 20 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) How much will you have in the account in 20 years?

This is a **future value of an ordinary annuity** problem. The formula for the future value of an ordinary annuity compounded monthly is:

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

Where:
- $P$ is the monthly deposit ($350),
- $r$ is the monthly interest rate (annual rate / 12),
- $n$ is the total number of deposits (years × 12).

Given:
- Monthly deposit $P = 350$,
- Annual interest rate = 8% or 0.08, so monthly interest rate $r = \frac{0.08}{12} = 0.0066667$,
- Number of months in 20 years $n = 20 \times 12 = 240$.

Now, I will calculate the future value (FV).

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

The total money you deposit is simply the monthly deposit multiplied by the number of months:

\[
\text{Total deposits} = P \times n
\]

### Part c) How much total interest will you earn?

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

\[
\text{Total interest} = FV - \text{Total deposits}
\]

Now, let me calculate these values.Here are the results:

a) The amount in the account after 20 years will be approximately **$206,157.15**.

b) The total amount of money you will deposit into the account is **$84,000**.

c) The total interest earned over 20 years will be approximately **$122,157.15**.

---

Would you like further details on any part of the solution? Here are some related questions you might consider:

1. What if the monthly deposit were $400 instead of $350?
2. How would the future value change if the interest rate was 5% instead of 8%?
3. How much would you earn in interest after only 10 years?
4. What would happen if you deposited annually instead of monthly?
5. How does the future value change if the interest is compounded quarterly?

**Tip:** Regularly contributing to a compounding interest account can significantly increase your total returns over time!

You deposit $350 each month into an account earning 8% interest compounded monthly. a) How much will you have in the account in 20 years? b) How much total money will you put into the account? c) How much total interest will you earn?

Calculate the future value of depositing $350 monthly into an account earning 8% interest compounded monthly. This problem uses the formula for the future value of an annuity, covering how much you will have after 20 years, total deposits, and interest earned. Ideal for Grades 10-12.

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