Question

The winner of the first annual Tom Morris Golf Invitational won $150 in the competition which was held in 1908. In 2015, the winner received $1,550,000. If the winner's purse continues to increase at the same interest rate, how much will the winner receive in 2042?

Answer 1

$ 15,532,522.20

Explanation:

Let r be the annual rate of increasing ( in percentage ),

Here, the winning amount on 1908, P = $ 150,

Number of years from 1908 to 2015, t = 107,

Thus, the winning amount in 2015,

`A=P(1+(r)/(100))^(107)`

`=150(1+(r)/(100))^(107)`

According to the question,

A = $1,550,000,

`\implies 1550000 = 150(1+(r)/(100))^(107)`

By graphing calculator,

`r\approx 0.09 = 9\%`

Now, the number of years from 1908 to 2042, t = 134,

Hence, the winning amount in 2042,

`A=150(1+(9)/(100))^(134)=\$15,532,522.2034\approx \$ 15,532,522.20`