In 1904, the first Putting Green Championship was held. The winner’s prize money
ID: 2718759 • Letter: I
Question
In 1904, the first Putting Green Championship was held. The winner’s prize money was $300. In 2009, the winner’s check was $1,560,000.
What was the annual percentage increase in the winner’s check over this period? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
If the winner’s prize increases at the same rate, what will it be in 2053? (Do not include the dollar sign ($). Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
In 1904, the first Putting Green Championship was held. The winner’s prize money was $300. In 2009, the winner’s check was $1,560,000.
Explanation / Answer
Requirement 1 Annual Growth % = ( ( f /s)1/y -1 ) *100 f = Final Value = 1560000 s = Starting Value = 300 y = Number of Years = 2009 - 1904 = 105 years Annual growth % =( ( 1560000/300)1/105 - 1) * 100 =( 1.0846 - 1 ) * 100 = 0.0846 * 100 = 8.46% Requirement 2 Using the same formulae as above , Annual Growth % = ( ( f /s)1/y-1 ) *100 = 8.46 = 0.0846 f = Final Value = x s = Starting Value = 1560000 y = Number of Years = 2053 - 2009 = 44 years 0.0846 = (x / 1560000)1/44 -1 1+ 0.0846 = (x / 1560000)0.02273 1.0846 = (x / 1560000)0.02273 root 0.02273 of 1.0846 = x/1560000 0.0236 = x/1560000 x = 0.0236 * 1560000 x = 0.0236 * 1560000 x = 36816 * 100 = 3681600 Hence if winner prize increases at the same rate then the prize money in 2053 = $ 3681600