Derek will deposit $3,882.00 per year for 14.00 years into an account that earns 10.00%. Assuming the first deposit is made 5.00 years from today, how much will be in the account 32.00 years from today?

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Answer format: Currency: Round to: 2 decimal places.

We can solve this problem in two steps: first, calculate the future value of the deposits made by Derek, and second, determine the future value of that amount after the deposits stop.

### Step 1: Future Value of an Annuity (Deposits)
Derek deposits \$3,882.00 every year for 14 years into an account that earns 10% interest. The first deposit is made 5 years from today. To calculate the future value of these deposits at the end of the 14 years, we will use the **Future Value of an Annuity Formula**:

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

Where:
- $FV$ is the future value of the annuity.
- $P = 3,882$ is the annual deposit.
- $r = 0.10$ is the annual interest rate.
- $n = 14$ is the number of years.

### Step 2: Future Value after Deposits Stop
After the 14 years of deposits, there will be 32 - (5 + 14) = 13 years remaining until 32 years from today. We need to calculate the value of the accumulated amount after 14 years and grow it for an additional 13 years.

The formula for future value after the deposits stop will be:

\[
FV_{total} = FV \times (1 + r)^t
\]

Where:
- $FV$ is the future value of the annuity from step 1.
- $t = 13$ is the number of years the amount grows after the deposits stop.
- $r = 0.10$ is the interest rate.

Now let's calculate the total future value.The total amount in Derek's account 32 years from today will be **\$374,912.81**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What if the interest rate was 8% instead of 10%?
2. How much would be in the account if Derek deposited for 20 years instead of 14?
3. What would be the total amount if Derek started depositing 10 years from today instead of 5?
4. How would the final amount change if the annual deposit was \$5,000 instead of \$3,882?
5. What if Derek made monthly deposits instead of yearly?

**Tip:** In compound interest problems, the timing of deposits has a significant effect on the final amount.

Derek will deposit $3,882.00 per year for 14.00 years into an account that earns 10.00%. Assuming the first deposit is made 5.00 years from today, how much will be in the account 32.00 years from today?

Calculate the future value of Derek's annual $3,882 deposits for 14 years, growing at 10% interest. Learn the steps to find out how much will be in his account 32 years from today using compound interest and annuity formulas.

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