In 1904, the first U.S. Open Golf Championship was held. The winner’s prize mone
ID: 2905831 • Letter: I
Question
In 1904, the first U.S. Open Golf Championship was held. The winner’s prize money was $240. In 2012, the winner’s check was $1,440,000.
What was the annual percentage increase in the winner’s check over this period? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
If the winner’s prize increases at the same rate, what will it be in 2036? (Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)
Requirement 1:What was the annual percentage increase in the winner’s check over this period? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
Explanation / Answer
1) Let FV ( future value ) = $ 1,440,000
PV ( present value) = $ 240
r ( rate) = ?
t ( time) = 2012 - 1904 = 108 yr
annual % increase in winner check ie r :
from FV formula
FV = PV( 1 + r)t
on solving this, r = ( FV / PV) 1/t - 1
r = ( 1,440,000 / 240 ) 1/108 - 1
r = 0.0838
r = 8.38 %
ii) winner's check in 2036:
FV = PV ( 1 + r) t
now PV = $ 1,440,000
r = 0.0838
t = 2036 - 2012 = 24 yr
so FV = 1,440,000 ( 1+ 0.0838 )24
FV = $ 9,890,503.58