Question

n 1904, the first Putting Green Championship was held. The winner's prize money was $160. In 2016, the winner's check was $1,165,000. (Do not round intermediate calculations.)

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 2049?

Answer 1

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Answer:

In 1904, the first Putting Green Championship was held. The winner’s prize money was M₁₉₀₄ = $160. In 2016, the winner’s check was M₂₀₁₆ = $1,165,000.

Time period, N = 2016 - 1904 = 112 years

Hence %age increase per year in the winner’s check over this period, g = (M₂₀₁₆ / M₁₉₀₄)^1/N - 1 = (1,165,000 / 160)^{1 / 112} - 1 = 8.26%

Hence, Increase per year: 8,26%

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If the winner’s prize increases at the same rate, what will it be in 2049?

Time period involved now, T = 2049 - 2016 = 33 years

Winner's prize in 2049 = M₂₀₁₆ x (1 + g)^T = 1,165,000 x (1 + 8.26%)³³ = $16,006,534.65

Hence, Winner's prize in 2049: $ 16,006,534.65