The future value of an investment of $7500 at interest rate r (in decimal form), compounded annually for 7 years, is given by: S=7500(1+r)^7 Use the root to find the rate r that will give a future value of $12900. Round to three decimal places as needed. Do NOT provide r as a percent!

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Answer to a math question The future value of an investment of $7500 at interest rate r (in decimal form), compounded annually for 7 years, is given by: S=7500(1+r)^7 Use the root to find the rate r that will give a future value of $12900. Round to three decimal places as needed. Do NOT provide r as a percent!

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Hermann

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126 Answers

12900 = 7500(1 + r)^7

Divide both sides by 7500:

\frac{12900}{7500} = (1 + r)^7

1.72 = (1 + r)^7

Take the 7th root of both sides:

1 + r = \sqrt[7]{1.72}

Using a calculator:

1 + r = 1.0788

Subtract 1 from both sides to find $ r $:

r = 1.0788 - 1

r = 0.0788

Rounding to three decimal places:

r \approx 0.079

Therefore,

r \approx 0.079

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