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

Answer:

$ 15,532,522.20

Step-by-step 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,

$A=P(1+\frac{r}{100})^{107}$

$=150(1+\frac{r}{100})^{107}$

According to the question,

A = $1,550,000,

$\implies 1550000 = 150(1+\frac{r}{100})^{107}$

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,

$A=150(1+\frac{9}{100})^{134}=\ 15,532,522.2034\approx \ 15,532,522.20$