QuestionAugust 27, 2025

To have 25,000 to spend on a new car in five years,how much money should Jill invest today at 8% compounded monthly? A. 5,000 B. 16,463 C. 16,780 D. 20,000

To have 25,000 to spend on a new car in five years,how much money should Jill invest today at 8% compounded monthly? A. 5,000 B. 16,463 C. 16,780 D. 20,000
To have 25,000 to spend on a new car in five years,how much money should Jill invest today at 8% compounded monthly? A. 5,000 B. 16,463 C. 16,780 D. 20,000

Solution
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Answer

C. \ 16,780 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 future value, P is the principal amount, 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 known values into the formula Given A = 25000, r = 0.08, n = 12, and t = 5. Substitute these into the formula to solve for P: \[ 25000 = P \left(1 + \frac{0.08}{12}\right)^{12 \times 5} \] 3. Calculate the compound factor Compute the compound factor: \[ \left(1 + \frac{0.08}{12}\right)^{60} \approx 1.48985 \] 4. Solve for the principal amount P Rearrange the formula to solve for P: \[ P = \frac{25000}{1.48985} \approx 16780 \]

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 future value, $P$ is the principal amount, $r$ 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 known values into the formula<br /> Given $A = 25000$, $r = 0.08$, $n = 12$, and $t = 5$. Substitute these into the formula to solve for $P$: <br />\[ 25000 = P \left(1 + \frac{0.08}{12}\right)^{12 \times 5} \]<br /><br />3. Calculate the compound factor<br /> Compute the compound factor: <br />\[ \left(1 + \frac{0.08}{12}\right)^{60} \approx 1.48985 \]<br /><br />4. Solve for the principal amount $P$<br /> Rearrange the formula to solve for $P$: <br />\[ P = \frac{25000}{1.48985} \approx 16780 \]
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