Reference no: EM132757836

In the following question can you please explain what the 41 and 31 are in the solution (the t)

Calculating Interest Rates and Future Values In 1968 prize money for the Wimbledon Tennis Championships was first awarded. The winner of the men's singles was £2,000 and for the ladies' singles it was £750. In 2016 both winners received £850,000. What was the percentage increase per year in the winner's cheque for men and women over this period? If the winner's prize increases at the same rate, what will the men's and ladies' singles tournament winners receive in 2040? 

Solutions

FV = PV(1 + r)^t

Solving for r, for men we get:

r = (FV / PV)^{1 / t} - 1

r = (£850,000 / £2,000)^1/41 - 1 = .1591 or 15.91%

Solving for r, for women we get:

r = (FV / PV)^{1 / t} - 1

r = (£850,000 / £750)^1/41 - 1 = .1871 or 18.71

To find the FV of the men's prize, we use:

FV = PV(1 + r)^t

FV = £850,000(1.1591)³¹ = £82,553,860 (based on unrounded values)

To find the FV of the women's prize, we use:

FV = PV(1 + r)^t

FV = £850,000(1.1871)³¹ = £173,305,085 (based on unrounded values)