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Problem 1

Find the accumulated amount $$A$$ if the principal $$P$$ is invested at the interest rate of $$r /$$ year for $$t$$ yr. $$P=\ 1000, r=7 \%, t=8, \text { compounded annually }$$

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The accumulated amount after 8 years with the given principal amount, interest rate, and compounding frequency is approximately $1,716.69. See the step by step solution Step by step solution Unlock all solutions Get unlimited access to millions of textbook solutions with Vaia Premium Over 22 million students worldwide already upgrade their learning with Vaia! Step 1: Identify the formula To find the accumulated amount, we will use the compound interest formula: $$A = P\left(1+\frac{r}{n}\right)^{nt}$$ where: - $$A$$ is the accumulated amount (including principal and interest), - $$P$$ is the principal amount (the initial amount invested), - $$r$$ is the annual interest rate (in decimal form), - $$t$$ is the time (in years), and - $$n$$ is the number of times interest is compounded per year. Since the interest is compounded annually, $$n$$ will be equal to 1. Step 2: Convert interest rate to decimal The given annual interest rate is 7%, so we need to convert it to decimal form by dividing by 100: $$r = \frac{7}{100} = 0.07$$ Step 3: Substitute the values into the formula Now, we will substitute the given values into the formula: $$P = 1000$$ $$n = 1$$ $$r = 0.07$$ $$t = 8$$ $$A = 1000\left(1+\frac{0.07}{1}\right)^{(1)(8)}$$ Step 4: Simplify and calculate the accumulated amount Next, simplify the formula and calculate the accumulated amount: $$A = 1000\left(1+0.07\right)^{8}$$ $$A = 1000(1.07)^{8}$$ Using a calculator, we find that: $$A \approx 1716.69$$ Step 5: State the final answer The accumulated amount after 8 years with the given principal amount, interest rate, and compounding frequency is approximately$1,716.69.

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