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.)

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.

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