QuestionJuly 14, 2025

Suppose that 2000 is invested at a rate of 3.8% compounded annually. Assuming that no withdrawals are made, find the total amount after 10 years. Do not round any intermediate computations, and round your answer to the nearest cent square

Suppose that 2000 is invested at a rate of 3.8% compounded annually. Assuming that no withdrawals are made, find the total amount after 10 years. Do not round any intermediate computations, and round your answer to the nearest cent square
Suppose that 2000 is invested at a rate of 3.8%  compounded annually. Assuming that no withdrawals are made, find the total amount after 10 years.
Do not round any intermediate computations, and round your answer to the nearest cent
 square

Solution
4.1(223 votes)

Answer

\2892.34 Explanation 1. Identify the Compound Interest Formula 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 Given Values Here, P = 2000, r = 0.038, n = 1, and t = 10. Substitute these values into the formula: A = 2000(1 + \frac{0.038}{1})^{1 \times 10}. 3. Calculate the Amount Simplify and calculate: A = 2000(1.038)^{10}. 4. Compute the Final Value Calculate (1.038)^{10} \approx 1.44617. Then, A = 2000 \times 1.44617 = 2892.34.

Explanation

1. Identify the Compound Interest Formula<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 Given Values<br /> Here, $P = 2000$, $r = 0.038$, $n = 1$, and $t = 10$. Substitute these values into the formula: $A = 2000(1 + \frac{0.038}{1})^{1 \times 10}$.<br /><br />3. Calculate the Amount<br /> Simplify and calculate: $A = 2000(1.038)^{10}$.<br /><br />4. Compute the Final Value<br /> Calculate $(1.038)^{10} \approx 1.44617$. Then, $A = 2000 \times 1.44617 = 2892.34$.
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