You deposit $100 each month into an account earning 7% interest compounded monthly.

a) How much will you have in the account in 30 years?

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

c) How much total interest will you earn?

Let's solve each part of the problem:

### Given:
- **Monthly deposit (P):** $100
- **Annual interest rate:** 7% or 0.07
- **Compounding frequency:** Monthly
- **Time period:** 30 years

### Definitions:
- **Monthly interest rate (r):** 
\[
r = \frac{0.07}{12} \approx 0.005833
\]
- **Total number of deposits (n):**
\[
n = 30 \times 12 = 360 \text{ months}
\]

### a) Future Value of the Account
The formula for the future value of an annuity with compound interest is:
\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Substituting the values:
\[
FV = 100 \times \frac{(1 + 0.005833)^{360} - 1}{0.005833}
\]

Let's calculate this:

\[
FV \approx 100 \times \frac{(1.005833)^{360} - 1}{0.005833}
\]
\[
FV \approx 100 \times \frac{10.744 - 1}{0.005833}
\]
\[
FV \approx 100 \times \frac{9.744}{0.005833}
\]
\[
FV \approx 100 \times 1670.95
\]
\[
FV \approx 167,095.00
\]

**Answer:** The amount in the account after 30 years will be approximately **$167,095.00**.

### b) Total Money Deposited

The total money deposited is simply the monthly deposit multiplied by the number of months:
\[
\text{Total Deposits} = 100 \times 360 = 36,000
\]

**Answer:** The total money deposited is **$36,000**.

### c) Total Interest Earned

The total interest earned is the difference between the future value and the total deposits:
\[
\text{Total Interest} = FV - \text{Total Deposits} = 167,095.00 - 36,000 = 131,095.00
\]

**Answer:** The total interest earned will be **$131,095.00**.

### Summary:
- **a)** Future value of the account: **$167,095.00**
- **b)** Total money deposited: **$36,000**
- **c)** Total interest earned: **$131,095.00**

Would you like any further explanations or have questions?

Here are some related questions:

1. How would the future value change if the interest rate were 8% instead of 7%?
2. What if you made quarterly deposits instead of monthly?
3. How much would the future value be after 25 years instead of 30 years?
4. What if the compounding frequency changed to quarterly or annually?
5. How much interest would you earn if you deposited $150 each month instead of $100?

**Tip:** Starting to save early makes a huge difference in how much your money grows, thanks to the power of compound interest!

Discover how to calculate the future value of compound interest with monthly deposits. Solve for the amount in the account after 30 years, total money deposited, and total interest earned with a 7% annual interest rate. Suitable for financial calculations and understanding compound interest.

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