QuestionAugust 8, 2025

Find the value of investing P dollars for n years with the interest rate r compounded annually. P= 600, r=5.6% , n=9years The final value is 987.12 (Round to the nearest cent as needed.)

Find the value of investing P dollars for n years with the interest rate r compounded annually. P= 600, r=5.6% , n=9years The final value is 987.12 (Round to the nearest cent as needed.)
Find the value of investing P dollars for n years with the interest rate r compounded annually. P= 600, r=5.6% , n=9years The final value is 987.12 (Round to the nearest cent as needed.)

Solution
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Answer

978.94 Explanation 1. Identify the Compound Interest Formula The formula for compound interest is **A = P(1 + \frac{r}{100})^n**, where A is the final amount, P is the principal, r is the annual interest rate, and n is the number of years. 2. Substitute Given Values Substitute P = 600, r = 5.6, and n = 9 into the formula: A = 600(1 + \frac{5.6}{100})^9. 3. Calculate the Interest Rate Factor Calculate 1 + \frac{5.6}{100} = 1.056. 4. Compute the Power Raise 1.056 to the power of 9: 1.056^9 \approx 1.63157. 5. Calculate the Final Amount Multiply by the principal: A = 600 \times 1.63157 \approx 978.94.

Explanation

1. Identify the Compound Interest Formula<br /> The formula for compound interest is **$A = P(1 + \frac{r}{100})^n$**, where $A$ is the final amount, $P$ is the principal, $r$ is the annual interest rate, and $n$ is the number of years.<br /><br />2. Substitute Given Values<br /> Substitute $P = 600$, $r = 5.6$, and $n = 9$ into the formula: <br /> $A = 600(1 + \frac{5.6}{100})^9$.<br /><br />3. Calculate the Interest Rate Factor<br /> Calculate $1 + \frac{5.6}{100} = 1.056$.<br /><br />4. Compute the Power<br /> Raise $1.056$ to the power of $9$: $1.056^9 \approx 1.63157$.<br /><br />5. Calculate the Final Amount<br /> Multiply by the principal: $A = 600 \times 1.63157 \approx 978.94$.
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