QuestionAugust 8, 2025

Suppose 5,000 is deposited into an account paying ng 7.5% interest, 7.5% compounded annually. How much money is in the account after four years if no withdrawals or additional deposits are made? 9,332.33 6,677.35 5,115.33 7,597.33

Suppose 5,000 is deposited into an account paying ng 7.5% interest, 7.5% compounded annually. How much money is in the account after four years if no withdrawals or additional deposits are made? 9,332.33 6,677.35 5,115.33 7,597.33
Suppose 5,000 is deposited into an account paying ng 7.5% interest, 7.5% compounded annually. How much money is in the account after four years if no withdrawals or additional deposits are made? 9,332.33 6,677.35 5,115.33 7,597.33

Solution
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Answer

\6,724.45 Explanation 1. Identify the formula for compound interest Use the formula for compound interest: **A = P(1 + \frac{r}{n})^{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 Here, P = 5000, r = 0.075, n = 1, and t = 4. Substitute these into the formula: A = 5000(1 + \frac{0.075}{1})^{1 \times 4}. 3. Calculate the expression Simplify the expression: A = 5000(1.075)^4. 4. Compute the final amount Calculate A = 5000 \times 1.34489 \approx 6724.45.

Explanation

1. Identify the formula for compound interest<br /> Use the formula for compound interest: **$A = P(1 + \frac{r}{n})^{nt}$**, 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<br /> Here, $P = 5000$, $r = 0.075$, $n = 1$, and $t = 4$. Substitute these into the formula: $A = 5000(1 + \frac{0.075}{1})^{1 \times 4}$.<br /><br />3. Calculate the expression<br /> Simplify the expression: $A = 5000(1.075)^4$.<br /><br />4. Compute the final amount<br /> Calculate $A = 5000 \times 1.34489 \approx 6724.45$.
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