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

Answer:

• a) 8.27%

Explanation

Given

• 1904, winner's prize money: $160

,

• 2016, winner's check: $1,167,000

Procedure

Using the following formula:

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

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:

$1,167,000=160(1+\frac{r}{100})^{112}$

Solving for r :

$(1+\frac{r}{100})^{112}=\frac{1,167,000}{160}$$(1+\frac{r}{100})^{112}=\frac{1,167,000}{160}$$\sqrt[112]{(1+\frac{r}{100})^{112}}=\sqrt[112]{\frac{1,167,000}{160}}$$\sqrt[112]{(1+\frac{r}{100})^{112}}=\sqrt[112]{\frac{1,167,000}{160}}$$1+\frac{r}{100}=\sqrt[112]{\frac{1,167,000}{160}}$$\frac{r}{100}=\sqrt[112]{\frac{1,167,000}{160}}-1$$r=(\sqrt[112]{\frac{1,167,000}{160}}-1)\times100\%$$r\approx8.27\%$