QuestionJuly 26, 2025

The Hill family wants to save money to travel the world. They purchase an annuity with a quarterly payment of 109 that earns 4.3% interest. compounded quarterly.Payments will be made at the end of each quarter. Find the total value of the annuity in 14 years. Do not round any intermediate computations, and round your final answer to the nearest cent.If necessary, refer to the list of financial formulas. square

The Hill family wants to save money to travel the world. They purchase an annuity with a quarterly payment of 109 that earns 4.3% interest. compounded quarterly.Payments will be made at the end of each quarter. Find the total value of the annuity in 14 years. Do not round any intermediate computations, and round your final answer to the nearest cent.If necessary, refer to the list of financial formulas. square
The Hill family wants to save money to travel the world. They purchase an annuity with a quarterly payment of 109 that earns 4.3% interest. compounded quarterly.Payments will be made at the end of each quarter. Find the total value of the annuity in 14 years. Do not round any intermediate computations, and round your final answer to the nearest cent.If necessary, refer to the list of financial formulas. square

Solution
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Answer

\7484.62 Explanation 1. Determine the number of periods Calculate total quarters in 14 years: 14 \times 4 = 56 quarters. 2. Calculate the periodic interest rate Convert annual interest rate to quarterly: \frac{4.3\%}{4} = 1.075\% = 0.01075. 3. Apply the future value of an annuity formula Use the formula for future value of an ordinary annuity: FV = P \left(\frac{(1 + r)^n - 1}{r}\right), where P = 109, r = 0.01075, and n = 56. Compute: FV = 109 \left(\frac{(1 + 0.01075)^{56} - 1}{0.01075}\right). 4. Calculate the future value Perform calculation: FV = 109 \left(\frac{(1.01075)^{56} - 1}{0.01075}\right). Result: FV = 109 \times 68.6937 = 7484.6203.

Explanation

1. Determine the number of periods<br /> Calculate total quarters in 14 years: $14 \times 4 = 56$ quarters.<br />2. Calculate the periodic interest rate<br /> Convert annual interest rate to quarterly: $\frac{4.3\%}{4} = 1.075\% = 0.01075$.<br />3. Apply the future value of an annuity formula<br /> Use the formula for future value of an ordinary annuity: $FV = P \left(\frac{(1 + r)^n - 1}{r}\right)$, where $P = 109$, $r = 0.01075$, and $n = 56$.<br /> Compute: $FV = 109 \left(\frac{(1 + 0.01075)^{56} - 1}{0.01075}\right)$.<br />4. Calculate the future value<br /> Perform calculation: $FV = 109 \left(\frac{(1.01075)^{56} - 1}{0.01075}\right)$.<br /> Result: $FV = 109 \times 68.6937 = 7484.6203$.
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