In 1895, the first Putting Green Championship was held. The winner’s prize money was $180. In 2016, the winner’s check was $1,500,000.

In 1895, the first Putting Green Championship was held. The winner’s prize money was $180. In 2016, the winner’s check was $1,500,000.
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 2045? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The time line is:

0		121
–$180		$1,500,000

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

    

FV = PV(1 + r)t

Solving for r, we get:

r = (FV/PV)1/t – 1

r = ($1,500,000/$180)1/121 – 1

r = .0775, or 7.75%

To find the FV of the first prize in 2045, we use:

  

0		29
–$1,500,000		FV

  

FV = PV(1 + r)t

FV = $1,500,000(1.077466)29

FV = $13,055,443.26

Calculator Solution:

Enter

121

±$180

$1,500,000

N

I/Y

PV

PMT

FV

Solve for

7.75%

Enter

29

7.7466%

±$1,500,000

N

I/Y

PV

PMT

FV

Solve for

$13,055,443.26