James deposits $1440.71$⁢1440.71 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $95,000$⁢95,000 in 1313 years. How much of the $95,000$⁢95,000 will James ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.

We can calculate the total amount James deposits and the interest earned by using the following steps:

### Step 1: Calculate the Total Deposits
James deposits \$1,440.71 each quarter for 13 years.

There are 4 quarters in a year, so over 13 years, the total number of deposits is:

\[
\text{Number of deposits} = 4 \times 13 = 52
\]

The total amount James deposits is:

\[
\text{Total deposits} = 1,440.71 \times 52
\]

### Step 2: Calculate the Interest Earned
The interest earned is the difference between the future value of the annuity and the total amount deposited. The future value of the annuity is \$95,000, so:

\[
\text{Interest earned} = \text{Future value} - \text{Total deposits}
\]

Now let's calculate these values.### Results:
1. **Total Deposits**: James will deposit \$74,916.92 into the account.
2. **Interest Earned**: The interest earned over the 13 years is \$20,083.08.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we calculate the interest rate required for this annuity?
2. What would happen if the deposit frequency changed (e.g., monthly instead of quarterly)?
3. How would the total interest change if James deposited more per quarter?
4. What if James wants to reach the same future value in 10 years instead of 13?
5. How would inflation affect the future value of the annuity?

**Tip**: Annuities grow faster with more frequent deposits due to compound interest, so increasing deposit frequency can lead to more interest earned.

James deposits $1,440.71 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $95,000 in 13 years. How much of the $95,000 will James ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.

Learn how to calculate total deposits and interest earned in an annuity account. James deposits $1,440.71 quarterly for 13 years to accumulate a future value of $95,000. This problem covers key concepts like annuities, interest calculation, and compound interest. Suitable for students in Grades 9-12.

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