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

Given the winner price cheque in 1895 is $230

In 2016 it was 1450000

Total Number of years passed over the period is 121 Years

It is pertinent to note that the prize money might have been increased at a constant rate be it inflation or any other factor relating to time value of money

We know the formula for future value of investment as

I * (1+r)ⁿ = Future value of investment

I = Initial Investment

r = rate of return

n = Number of years

Hence ,

(1+r)ⁿ * 230 = 1450000

(1+r)ⁿ = (6304.348783)

1+r = (6304.348783)^1/121

Hence r = 0.074983963

a) The percentage increase is 7.498396% per year

b) Amount it will be in 2020

1450000 * (1.074984)¹⁴ = $3990210