QuestionJuly 17, 2025

Amy borrowed 8000 at a rate of 7.5% compounded monthly. Assuming she makes no payments, how much will she owe after 8 years? Do not round any intermediate computations, and round your answer to the nearest cent. 13515.83

Amy borrowed 8000 at a rate of 7.5% compounded monthly. Assuming she makes no payments, how much will she owe after 8 years? Do not round any intermediate computations, and round your answer to the nearest cent. 13515.83
Amy borrowed 8000 at a rate of 7.5% compounded monthly. Assuming she makes no payments, how much will she owe after 8 years? Do not round any intermediate computations, and round your answer to the nearest cent. 13515.83

Solution
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Answer

\13515.83 Explanation 1. Identify the formula for compound interest Use the formula for compound interest: **A = P \left(1 + \frac{r}{n}\right)^{nt}**, where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. 2. Substitute the given values into the formula Here, P = 8000, r = 0.075, n = 12, and t = 8. Substitute these into the formula: A = 8000 \left(1 + \frac{0.075}{12}\right)^{12 \times 8}. 3. Calculate the monthly interest rate Compute \frac{0.075}{12} = 0.00625. 4. Calculate the exponent Compute 12 \times 8 = 96. 5. Calculate the compound factor Compute \left(1 + 0.00625\right)^{96}. 6. Calculate the final amount Multiply the principal by the compound factor: A = 8000 \times (1.00625)^{96}. 7. Round the result to the nearest cent Calculate the exact value and round it to two decimal places.

Explanation

1. Identify the formula for compound interest<br /> Use the formula for compound interest: **$A = P \left(1 + \frac{r}{n}\right)^{nt}$**, where $A$ is the amount, $P$ is the principal, $r$ is the annual interest rate, $n$ is the number of times interest is compounded per year, and $t$ is the time in years.<br /><br />2. Substitute the given values into the formula<br /> Here, $P = 8000$, $r = 0.075$, $n = 12$, and $t = 8$. Substitute these into the formula: $A = 8000 \left(1 + \frac{0.075}{12}\right)^{12 \times 8}$.<br /><br />3. Calculate the monthly interest rate<br /> Compute $\frac{0.075}{12} = 0.00625$.<br /><br />4. Calculate the exponent<br /> Compute $12 \times 8 = 96$.<br /><br />5. Calculate the compound factor<br /> Compute $\left(1 + 0.00625\right)^{96}$.<br /><br />6. Calculate the final amount<br /> Multiply the principal by the compound factor: $A = 8000 \times (1.00625)^{96}$.<br /><br />7. Round the result to the nearest cent<br /> Calculate the exact value and round it to two decimal places.
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