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.