Question

Check my work Check My Work button is now disabledItem 2Item 2 16.66 points In 1901, the first Green Jacket Golf Championship was held. The winner’s prize money was $330. In 2015, the winner’s check was $1,690,000. What was the annual percentage increase 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.) Annual percentage % If the winner’s prize increases at the same rate, what will it be in 2050? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The annual percentage increase in the winner’s check over this period was 7.78%

It will be $23,266,067.23 in 2050

Explanation:

As per given data

Value of lottery in 1901 = $330

Winner's Check in 2015 = $1,690,000

Numbers of Years = 2015 - 1901 = 114 years

Use following formula to calculate annual percentage increase

Future value = Present value  x ( 1 + annual percentage increase)^numbers of years

Where

Future value is Winner's Check value in 2015

Present value is Value of lottery in 1901

Place values in the formula

$1,690,000 = $330 x ( 1 + annual percentage increase)^114

$1,690,000 / $330 = ( 1 + annual percentage increase)^114

5,121.21 =  ( 1 + annual percentage increase)^114

( 5,121.21 )^1/114 = 1 + annual percentage increase

1.0778 = 1 + annual percentage increase

Annual percentage increase = 1.0778 - 1

Annual percentage increase = 0.0778

Annual percentage increase = 7.78%

Use following formula to calculate the value in 2015

Future value = Present value  x ( 1 + annual percentage increase)^numbers of years

Where

Present value = $1,690,000

Future value =?

Annual Percentage increase = 7.78%

Numbers of years = 2050 - 2015 = 35 Years

Place the value in the formula

Future value = $1,690,000  x ( 1 + 7.78% )^35

Future value = $23,266,067.23