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## Chapter 2: Chapter 2

Problem 10

# Calculate, to the nearest cent, the future value of an investment of $\$ 10,000$at the stated interest rate after the stated amount of time. [HINT: See Quick Examples 1 and $$2 .$$. $$11.2 \%$$ per year, compounded monthly, after 12 years ### Short Answer Expert verified The future value of the investment after 12 years is approximately $$\39,712.37$$, rounded to the nearest cent. 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: Convert annual interest rate to decimal form To convert the annual interest rate (11.2%) to decimal form, divide the percentage by 100: $$r = \frac{11.2}{100} = 0.112$$ ## Step 2: Identify the given values Now that we have the annual interest rate in decimal form, let's list all the given values: - $$PV = \10,000$$ - $$r = 0.112$$ - $$n = 12$$ (compounded monthly) - $$t = 12$$ years ## Step 3: Calculate the future value Using the future value formula for compound interest and the values from Step 2, we can compute the future value of the investment: $FV = PV(1 + \frac{r}{n})^{nt}$ $FV = 10000(1 + \frac{0.112}{12})^{12 \cdot 12}$ $FV = 10000(1 + 0.009333)^{144}$ $FV = 10000(1.009333)^{144}$ $FV ≈ \39,712.37$ The future value of the investment after 12 years is approximately$39,712.37, rounded to the nearest cent.

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