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Starting at age 50 and continuing to age 65, Stephen deposited $5333.33 every quarter into a retirement account that averaged 6% interest. At age 65, he had $513,144.49 in his account.

(a. How much did Stephen deposit into his retirement account?
(b. How much interest did Stephen earn?

User OCcSking
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Final answer:

Stephen deposited a total of $320,000 into his retirement account by making quarterly payments of $5333.33 for 15 years. The total interest earned on his deposits was $193,144.49, calculated by subtracting the total deposits from the final account balance of $513,144.49.

Step-by-step explanation:

The question involves calculating the total deposits made by Stephen into his retirement account and the amount of interest earned over a period of time. To calculate these values, we must understand the concepts of regular deposits and compound interest.

Calculating the Total Deposits

Stephen deposited $5333.33 every quarter from age 50 to age 65. Since a quarter is 3 months long, there are four quarters in a year. Therefore, he made deposits for 15 years, which is equivalent to 15 x 4 = 60 quarters.

Total deposits = Number of deposits × Deposit amount per quarter

Total deposits = 60 × $5333.33

Total deposits = $320,000.

Calculating the Interest Earned

To calculate the interest earned, we take the final account value and subtract the total deposits from it.

Interest earned = Final account balance - Total deposits

Interest earned = $513,144.49 - $320,000

Interest earned = $193,144.49.

Through this exercise, it's clear that making regular deposits into a retirement account and allowing the power of compound interest to work can significantly increase the value of savings over time.

User Rabbott
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