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

(i) 7.54%(Approx).

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

Step-by-step explanation:

Given that,

Winner’s prize money = $220

In 2016,

Winner’s check = $1,460,000

We use the formula:

`A=P(1+(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+(r)/(100) )^(n)`

`((1,460,000)/(220))^{(1)/(121) }=(1+(r)/(100))`

(1+r/100) = 1.075440035

r = (1.075440035 - 1) × 100

= 7.54%(Approx).

(b)

n = 2041 - 2016

= 25

`A=P(1+(r)/(100) )^(n)`

`A=1,460,000(1+0.075440035)^(25)`

= 1,460,000 × 6.161053698

= $8,995,138.42(Approx).