What is the rate of return on an investment of 10,000 that will be worth 11,576 in three years?

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Multiple Choice

What is the rate of return on an investment of 10,000 that will be worth 11,576 in three years?

Explanation:
Finding the annual rate of return with annual compounding. You want r such that the initial 10,000 grows to 11,576 over three years, using the formula FV = PV × (1 + r)^n. So 10,000 × (1 + r)^3 = 11,576, which gives (11,576 / 10,000)^(1/3) − 1. The ratio is 1.1576. The cube root of 1.1576 is about 1.05 because 1.05^3 = 1.157625. Therefore r ≈ 0.05, or 5% per year.

Finding the annual rate of return with annual compounding. You want r such that the initial 10,000 grows to 11,576 over three years, using the formula FV = PV × (1 + r)^n. So 10,000 × (1 + r)^3 = 11,576, which gives (11,576 / 10,000)^(1/3) − 1. The ratio is 1.1576. The cube root of 1.1576 is about 1.05 because 1.05^3 = 1.157625. Therefore r ≈ 0.05, or 5% per year.

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