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What amount of money must you invest at $6.8\%$ compounded monthly, in order to have $\$10,000$ after $10$ years? Round your answer to the nearest dollar.

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Exponential growth and decay: word problems

Full solution

Q. What amount of money must you invest at

6.8\%

compounded monthly, in order to have

\$10,000

after

10

years? Round your answer to the nearest dollar.

Identify formula for compound interest: Identify the formula for compound interest: $A = P(1 + r/n)^{(nt)}$ . Here, $A = \$10,000$ , $r = 6.8\%$ or $0.068$ , $n = 12$ (monthly), $t = 10$ years.
Convert percentage to decimal: Convert the percentage to a decimal: $r = 6.8\% = 0.068$ .
Plug values into formula: Plug the values into the formula and solve for $P$ : $10000 = P(1 + 0.068/12)^{(12\times10)}$ .
Calculate growth factor: Calculate the growth factor: $(1 + \frac{0.068}{12})^{(12\times10)}$ .
Do the math: Do the math: $(1 + 0.068/12)^{120} = (1 + 0.0056667)^{120}$ .
Use calculator to find value: Use a calculator to find the value: $(1.0056667)^{120} \approx 1.984$ .
Divide by growth factor: Divide $\$10,000$ by the growth factor: $\frac{10000}{1.984} \approx 5040.32$ .
Round answer to nearest dollar: Round the answer to the nearest dollar: $\$5040$ .

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