Problem 5-13 Calculating Interest Rates and Future Values [LO1, 3] In 1895, the

Question

Problem 5-13 Calculating Interest Rates and Future Values [LO1, 3] In 1895, the first Putting Green Championship was held. The winner's prize money was $160. In 2016, the winner's check was $1,400,000. o. What was the percentage increase per year in the winner's check over this iod? (Do not round intermediate calculations and enter your answer a rounded to 2 decimal places, e.g., 3216.) If the winner's prize increases at the same rate, what will it be in 2 b. 047? (Do not calculations and round your answer to 2 decimal places, e.g. 32.16.) a. Increase per year b. Winners prize in 2047

Explanation / Answer

This question requires application of basic Time value of money function: FV = PV * (1 + r)n

a) Calculating rate of increase.

FV = $1,400,000

n = 2016 - 1895 = 121

PV = $160

1,400,000 = 160 * (1 + r)121

8750 = (1 + r)121

Taking 121th root of both sides

1 + r = 1.0779

r = 7.79% --> Answer to part 1

b) Calculating the prize money in 2047

PV = $1,400,000

r = 7.79%

n = 2047 - 2016 = 31

FV = ?

FV = 1400000 * (1 + 7.79%)31

FV = 1400000 * 10.2314

FV = $14,323,989.14

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