Questions: Ravi plans to set aside money for his young daughter's college tuition. He will deposit money in an ordinary annuity that earns 2.4% interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money does he need to deposit into the annuity each quarter for the annuity to have a total value of 73,000 after 15 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Ravi plans to set aside money for his young daughter's college tuition. He will deposit money in an ordinary annuity that earns 2.4% interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money does he need to deposit into the annuity each quarter for the annuity to have a total value of 73,000 after 15 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: Ravi plans to set aside money for his young daughter's college tuition. He will deposit money in an ordinary annuity that earns $2.4 \%$ interest, compounded quarterly. Deposits will be made at the end of each quarter. How much money does he need to deposit into the annuity each quarter for the annuity to have a total value of $\$ 73,000$ after 15 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. $\square$
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Solution

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Solution Steps

Step 1: Convert the annual interest rate to the periodic interest rate

To find the periodic interest rate, divide the annual interest rate by the number of compounding periods per year: $i = \frac{r}{n} = \frac{0.024}{4} = 0.006.$

Step 2: Calculate the total number of compounding periods

The total number of compounding periods is calculated by multiplying the total years by the number of compounding periods per year: $N = n \times t = 4 \times 15 = 60.$

Step 3: Solve for the periodic payment (PMT)

Using the future value of an ordinary annuity formula: $PMT = \frac{FV \times i}{(1 + i)^N - 1} = \frac{73000 \times 0.006}{(1 + 0.006)^60 - 1} = 1014.39.$

Final Answer:

The periodic payment needed to reach a future value of $73000 given an annual interest rate of 2.4%, compounded 4 times per year, over a total period of 15 years is approximately $1014.39.

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