QuestionAugust 9, 2025

Carmen deposits 7,500 in a savings account with 3.25% interest compounded annually.After three years, approximately how much money will be in Carmen's account? 7,744 8,229 8,275 8,472

Carmen deposits 7,500 in a savings account with 3.25% interest compounded annually.After three years, approximately how much money will be in Carmen's account? 7,744 8,229 8,275 8,472
Carmen deposits 7,500 in a savings account with 3.25% interest compounded annually.After three years, approximately how much money will be in Carmen's account? 7,744 8,229 8,275 8,472

Solution
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Answer

\8,275 Explanation 1. Identify the formula for compound interest Use **A = P(1 + \frac{r}{n})^{nt}** where A is the amount, P is the principal, r is the rate, n is the number of times interest applied per time period, and t is the time. 2. Substitute the given values Here, P = 7500, r = 0.0325, n = 1, and t = 3. Substitute these into the formula: A = 7500(1 + \frac{0.0325}{1})^{1 \times 3}. 3. Calculate the expression Simplify: A = 7500(1.0325)^3. Calculate: A \approx 7500 \times 1.1006 \approx 8254.5.

Explanation

1. Identify the formula for compound interest<br /> Use **$A = P(1 + \frac{r}{n})^{nt}$** where $A$ is the amount, $P$ is the principal, $r$ is the rate, $n$ is the number of times interest applied per time period, and $t$ is the time.<br />2. Substitute the given values<br /> Here, $P = 7500$, $r = 0.0325$, $n = 1$, and $t = 3$. Substitute these into the formula: $A = 7500(1 + \frac{0.0325}{1})^{1 \times 3}$.<br />3. Calculate the expression<br /> Simplify: $A = 7500(1.0325)^3$.<br /> Calculate: $A \approx 7500 \times 1.1006 \approx 8254.5$.
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