You deposit $400 each month into an account earning 8% interest compounded monthly.

a) How much will you have in the account in 25 years?
b) How much total money will you put into the account?                                                c) How much total interest will you earn?

We can solve this problem using the formula for the future value of an ordinary annuity, which is used when you make regular payments into an account with compound interest.

The future value of an ordinary annuity is given by:

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

Where:
- $ P $ = monthly deposit amount ($400)
- $ r $ = monthly interest rate (annual rate divided by 12)
- $ n $ = total number of payments (number of years times 12)

### Step 1: Calculate future value (a)

Given:
- Monthly deposit ($ P $) = $400
- Annual interest rate = 8%, so the monthly interest rate is $ r = \frac{8\%}{12} = 0.00667 $
- Time = 25 years, so $ n = 25 \times 12 = 300 $ months

Plugging these values into the formula:

\[
FV = 400 \times \frac{(1 + 0.00667)^{300} - 1}{0.00667}
\]

Let's calculate the future value.

### Step 2: Calculate total money deposited (b)

The total amount of money you deposit over the 25 years is:

\[
\text{Total Deposits} = P \times n = 400 \times 300 = 120,000
\]

### Step 3: Calculate total interest earned (c)

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

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

Now, I'll calculate the results.### a) Future Value (Amount in the account after 25 years):
The future value of the account after 25 years is approximately **$380,410.56**.

### b) Total Money Deposited:
The total amount of money you will have deposited into the account over 25 years is **$120,000**.

### c) Total Interest Earned:
The total interest earned over the 25 years is approximately **$260,410.56**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What if the interest rate was compounded annually instead of monthly?
2. How would the future value change if you deposited $500 per month?
3. What if you only deposited money for 20 years instead of 25?
4. How much would you have if the interest rate was 6% instead of 8%?
5. What if you withdrew some amount periodically from the account?

**Tip:** The power of compound interest grows significantly over long periods; early and consistent investing can dramatically increase future savings.

You deposit $400 each month into an account earning 8% interest compounded monthly.

a) How much will you have in the account in 25 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 monthly deposits of $400 into an account earning 8% interest compounded monthly for 25 years. Understand key financial concepts such as compound interest, total deposits, and total interest earned with a step-by-step solution.

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