The prize money for the winner of the US Open Golf Championship has increased fr

Question

The prize money for the winner of the US Open Golf Championship has increased from $1.35 Million when Tiger Woods won in 2008 to $1.8 Million when Dustin Johnson won last year (2016). During the same time period, the CPI value has increased from 218.8 in June 2008 to 241.0 in June 2016.

(a) Calculate the average annual rate of increase in the prize money over that period.

(b) Calculate the corresponding average annual general inflation rate over the time period.

(c) Hence, calculate the “real” annual rate of increase in the prize money taking into account the general inflation rate over the time period.

(d) Calculate Dustin Johnson’s prize money in “2008” dollars.

Explanation / Answer

Number of years between 2008 and 2016 is 8.

(a) If average annual rate of increase be R%, then

$1.35 million x (1 + R)8 = $1.8 million

(1 + R)8 = $1.8 million / $1.35 million = 1.3333

Taking 8th root on each side,

1 + R = 1.0366

R = 0.0366

R = 3.66%

(b) Inflation rate is measured by % increase in CPI. If average annual rate of increase of CPI be R%, then

218.8 x (1 + R)8 = 241

(1 + R)8 = 241 / 218.8 = 1.1015

Taking 8th root on each side,

1 + R = 1.0122

R = 0.0122

R = 1.22%

(c) Real rate of increase = Average annual increase in prize money - Average annual increase in inflation

= 3.66% - 1.22%

= 2.44%

(d) Prize money in 2008 dollars = Prize money in 2016 x (CPI in 2008 / CPI in 2016)

= $1.8 million x (218.8 / 241)

= $1.63 million

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