Kevin deposits $1423.62$⁢1423.62 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $85,000$⁢85,000 in 1212 years. How much of the $85,000$⁢85,000 will Kevin ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.


We can solve this problem using the following steps:

### Step 1: Determine Kevin's total deposit over the 12-year period.

Since Kevin deposits $1,423.62 each quarter, we need to calculate the total number of quarters in 12 years and multiply it by the quarterly deposit amount.

\[
\text{Number of quarters} = 12 \, \text{years} \times 4 \, \text{quarters per year} = 48 \, \text{quarters}
\]

So, the total amount deposited by Kevin is:

\[
\text{Total deposit} = 48 \, \text{quarters} \times 1,423.62 \, \text{dollars per quarter} = 68,333.76 \, \text{dollars}
\]

### Step 2: Calculate the interest earned.

Kevin wants to accumulate a future value of $85,000. To find the interest, we subtract the total amount deposited from the future value:

\[
\text{Interest earned} = 85,000 - 68,333.76 = 16,666.24 \, \text{dollars}
\]

### Final Answer:
- **Total amount deposited by Kevin**: $68,333.76
- **Interest earned**: $16,666.24

Would you like more details on how to compute the future value in similar annuity problems?

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**Related Questions**:
1. How is the future value of an annuity calculated using interest rates?
2. What is the formula for calculating interest in compound interest accounts?
3. How would Kevin's total deposit change if he contributed monthly instead of quarterly?
4. What would happen to the interest earned if Kevin invested in a higher-yielding account?
5. How can Kevin calculate the required quarterly deposit to reach a different future goal?

**Tip**: Understanding annuities is useful in retirement planning, as it helps to calculate future financial security based on periodic deposits.

Kevin deposits $1,423.62 each quarter into an annuity account for his child's college fund in order to accumulate a future value of $85,000 in 12 years. How much of the $85,000 will Kevin ultimately deposit in the account, and how much is interest earned?

Learn how to calculate the future value of an annuity and the interest earned. Kevin deposits $1,423.62 each quarter for 12 years to reach $85,000. This problem explains the concepts of future value and compound interest, including step-by-step calculations. Ideal for students in Grades 9-12.

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