Questions: Walter deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of 85,000 in 18 years. Assuming an APR of 3.1% compounded monthly, how much is interest earned? Round your answers to the nearest cent, if necessary.

Walter deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of 85,000 in 18 years. Assuming an APR of 3.1% compounded monthly, how much is interest earned? Round your answers to the nearest cent, if necessary.

Transcript text: Walter deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of $85,000 in 18 years. Assuming an APR of 3.1% compounded monthly, how much is interest earned? Round your answers to the nearest cent, if necessary.

Solution

Solution Steps

Step 1: Calculating the Periodic Interest Rate

The periodic interest rate (r) is calculated as APR/n, which is 3.1% / 12 = 0.26% per period.

Step 2: Calculating the Total Number of Compounding Periods

The total number of compounding periods (nt) is n * t, which is 12 * 18 = 216.

Step 3: Using the Known Deposit Amount (PMT)

The deposit amount (PMT) is known and is 294.38.

Step 4: Calculating the Total Amount Deposited

Total Deposits = PMT * n * t, which gives Total Deposits = 63586.08.

Step 5: Calculating the Interest Earned

Interest Earned = FV - Total Deposits, which gives Interest Earned = 21413.92.

Final Answer:

The total amount deposited is 63586.08, and the interest earned is 21413.92.

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