Problem 4-13 Calculating Interest Rates and Future Values [LO 1, 3] In 1907, the

Question

Problem 4-13 Calculating Interest Rates and Future Values [LO 1, 3] In 1907, the first U.S. Open Golf Championship was held. The winner's prize money was $270. In 2012, the winner's check was $1,470,000. 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).) Annual percentage 8.54 % Requirement 2: If the winner's prize increases at the same rate, what will it be in 2033? (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).) Prize money S 8,220,344.7

Explanation / Answer

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

a.

1,470,000=270*(1+r/100)^105

(1,470,000/270)^(1/105)=(1+r/100)

(1+r/100)=1.08537674

r=(1.08537674-1)*100

=8.54%(Approx).

b.

Hence

A=$1,470,000(1+0.08537674)^21

=$1,470,000*5.587154944

which is equal to

=$8,213,117.74(Approx).

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