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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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