Question

SavedIn 1904, the first Putting Green Championship was held. The winner's prize money was $160. In 2016, the winner's check was $1,167,000. (Do not round intermediate calculations.)a. What was the percentage increase per year in the winner's check over this period?

Answer 1

• a) 8.27%

Step-by-step explanation

Given

• 1904, winner's prize money: $160

,

• 2016, winner's check: $1,167,000

Procedure

Using the following formula:

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

where A is the future value, P the present value, r the rate of interest, n the time period.

• a)

Considering that n = 2016 – 1904 = 112:

`1,167,000=160(1+(r)/(100))^(112)`

Solving for r :

`(1+(r)/(100))^(112)=(1,167,000)/(160)`
`(1+(r)/(100))^(112)=(1,167,000)/(160)`
`\sqrt[112]{(1+(r)/(100))^(112)}=\sqrt[112]{(1,167,000)/(160)}`
`\sqrt[112]{(1+(r)/(100))^(112)}=\sqrt[112]{(1,167,000)/(160)}`
`1+(r)/(100)=\sqrt[112]{(1,167,000)/(160)}`
`(r)/(100)=\sqrt[112]{(1,167,000)/(160)}-1`
`r=(\sqrt[112]{(1,167,000)/(160)}-1)*100\%`
`r\approx8.27\%`