Question

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an amount of $38,000 is borrowed for 8 years at 8.5% interest, compounded annually. assuming that no payments are made, find the amount owed after 8 years.
use the calculator provided and round your answer to the nearest dollar.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the number of years.

Step2: Identify values

Here, $P = 38000$, $r = 0.085$ (since $8.5\% = \frac{8.5}{100}=0.085$), and $t = 8$.

Step3: Substitute into formula

Calculate $A = 38000\times(1 + 0.085)^8$. First, compute $(1 + 0.085)=1.085$. Then, calculate $1.085^8$. Using a calculator, $1.085^8\approx1.8113616$. Then, multiply by 38000: $38000\times1.8113616\approx68831.74$.

Step4: Round to nearest dollar

Rounding $68831.74$ to the nearest dollar gives $68832$.

Answer:

$\$68832$