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 $230. In 2016, the winner’s check was $1,450,000.

  

a.	What was the percentage increase per year in the winner’s check over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If the winner’s prize increases at the same rate, what will it be in 2030? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a)

Number of periods = 2016 - 1895 = 121

percentage increase per year = (Future value / initial value)^1/n - 1

percentage increase per year = (1,450,000 / 230)^1/121 - 1

percentage increase per year = (6,304.347826)^1/121 - 1

percentage increase per year = 1.0750 - 1

percentage increase per year = 0.0750 or 7.50%

b)

Number of periods = 2030 - 2016 = 14

Future value = Present value (1 + r)^n

Future value = 1,450,000 (1 + 0.074984)^14

Future value = 1,450,000 * 2.751871

Future value = $3,990,212.33