Question

In 1895, the first U.S. Open Golf Championship was held. The winner’s prize money was $150. In 2016, the winner’s check was $1,800,000.
1. 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.)
2. If the winner’s prize increases at the same rate, what will it be in 2040? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

1.  The percentage increase per year in the winner’s check over the period: 8.07%.

2. If the winner’s prize increases at the same rate, the prize will be $11,593,008.13 in 2040.

Explanation:

1.

We use the formula for Compound Annual Growth Rate (CAGR) to sovle the problem:

From 1895 to 2016, there are: 2016 - 1895 = 121 compounding periods;

Thus, the CAGR over the period is calculated as: (1,800,000/150)^(1/121) - 1 = 8.07%.

2.

From 2016 to 2040, there are: 2040 - 2016 = 24 compounding periods.

Thus, the winner’s prize in 2040 given the same rate of increasing will be:

1,800,000 * (1+8.07%)^24 = $11,593,008.13.