Question

In 1895, the first Putting Green Championship was held. The winner’s prize money was $220. In 2016, the winner’s check was $1,460,000. 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 2041? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

(i) 7.54%(Approx).

(ii) $8,995,138.42(Approx).

Explanation:

Given that,

Winner’s prize money = $220

In 2016,

Winner’s check = $1,460,000

We use the formula:

$A=P(1+\frac{r}{100} )^{n}$

Where ,

A=future value

P=present value

r=rate of interest

n=time period.

n = 2016 - 1895

  = 121

(a)

$1,460,000=220(1+\frac{r}{100} )^{n}$

$(\frac{1,460,000}{220})^{\frac{1}{121} }=(1+\frac{r}{100})$

(1+r/100) = 1.075440035

r = (1.075440035 - 1) × 100

 = 7.54%(Approx).

(b)

n = 2041 - 2016

  = 25

$A=P(1+\frac{r}{100} )^{n}$

$A=1,460,000(1+0.075440035)^{25}$

         = 1,460,000 × 6.161053698

         = $8,995,138.42(Approx).