Questions: Frank has always dreamed of opening a café by the seaside. He decides he will save to help open the café by depositing money in an ordinary annuity at 6.6% interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money will he need to deposit into the annuity each quarter for the annuity to have a total value of 25,000 after 7 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Frank has always dreamed of opening a café by the seaside. He decides he will save to help open the café by depositing money in an ordinary annuity at 6.6% interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money will he need to deposit into the annuity each quarter for the annuity to have a total value of 25,000 after 7 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.
Transcript text: Frank has always dreamed of opening a café by the seaside. He decides he will save to help open the café by depositing money in an ordinary ann $6.6 \%$ interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money will he need to deposit into the annuity each quarter for the annuity to have a total value of $\$ 25,000$ after 7 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.
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Solution

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Solution Steps

Step 1: Convert the annual interest rate to a decimal

The annual interest rate 6.6% is converted to a decimal by dividing by 100: \(r = 0.066\).

Step 2: Calculate the periodic interest rate

The periodic interest rate is calculated as \(i = \frac{r}{n} = \frac{0.066}{4} = 0.0165\).

Step 3: Calculate the total number of compounding periods

The total number of compounding periods is \(N = n \times t = 4 \times 7 = 28\).

Step 4: Use the future value of an ordinary annuity formula to find the periodic payment

Using the formula \(P = \frac{FV}{\frac{(1 + i)^N - 1}{i}}\), we find that the periodic payment is \(P = 709.65\).

Final Answer:

The periodic payment that needs to be deposited each period is $709.65.

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