In 1895 the first a sporting event was held The winners priz

In 1895, the first a sporting event was held. The winner\'s prize money was $140. In 2007, the winner\'s check was $1,174,000. (Do not round your intermediate calculations.)

Required:

(a) What was the percentage increase per year in the winner\'s check over this period?

(b) If the winner\'s prize increases at the same rate, what will it be in 2040?

Solution

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period

1.

1,174,000=140(1+r/100)^112

(1,174,000/140)^(1/112)=(1+r/100)

(1+r/100)=1.08401

r=(1.08401-1)*100

=8.40%(Approx).

2.

A=$1,174,000(1+8.40/100)^33

=$1,174,000*14.32329886

which is equal to

=$16,815,552.86(Approx).