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A $10,000 investment earned $2,000 interest after 39 months of semiannual compounding

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A $10,000 investment earned $2,000 interest after 39 months of semiannual compounding. What effective rate of return did the investment earn?

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Future value = Investment + Interest

= 10000 + 2000

= 12000

Rate of return per semi annual period = (FV / Initial investment)^(1/N) -1

where N = 39/6 = 6.50

Rate = (12000/1000)^(1/6.50) - 1

= 2.84466%

Effective rate of return = (1 + 2.84466%)^2 - 1

= 5.77%

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