Please help. I can\'t figure out how to solve this. Thank you! Time Value Person

Question

Please help. I can't figure out how to solve this. Thank you!

Time Value Personal Finance Problem Misty needs to have $14,000 at the end of 7 years to fulfill her goal of purchasing a small sailboat. She is willing to invest a lump sum today and leave the money untouched for 7 years until it grows to $14,000, but she wonders what sort of investment return she will need to earn to reach her goal. Use your calculator or spreadsheet to figure out the annually compounded rate of return needed if she can invest $9,500 today. The annually compounded rate of return Misty needs to earn to reach her goal is square %. (Round to two decimal places.)

Explanation / Answer

Value of investment Today = $9,500

Value after 7 year = $14,000

Interest rate on investment is calculated below:

Let’s assume interest rate = r

$14,000 = $9,500 × (1 + r) ^7

$14,000 / $9,500 = (1 + r) ^7

1.4737 = (1 + r) ^7

(1.4737)^ (1/7) = 1 + r

1 + r = 1.05695

r = 5.7%

Hence, interest rate in investment is 5.7%.

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