Question

In 1895, the first Putting Green Championship was held. The winner's prize money was $160 in 2016, the winner's check was $1.360.000, a. What was the percentage increase per year in the winner's check over this period? (Do not found intermediate calculations and 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 2039? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g. 32.16.) increase per year b. Winners prize in 2039

Answer 1

(a) Suppose Prize money received at the beginning of the year of 1895 and In 2016 at the end of year the prize money would become $ 136000.

So from 1895 to 2016 total no. of years = 2016 -1895 =121 + 1(1895th Year)

= 122 Years

Formula of compounding interest rate C.I = Principal*(1+interest rate)^(No. of years)

Put the values in formula Where C.I = 136000

interest rate = ?

No. of years = 122

136000 = 160*(1+i)^122

136000/160 = (1+i)^122

850 = (1+i)^122

take (1/122) of both sides

850^(1/122) = 1+i

1.056846 = 1+i

i = 1.056846-1

= 0.056846

= 5.685%

(b) Calculation of the prize money at the end of year 2039

No of years = 2039 - 1845 = 144 + 1

= 145

i = 5.685%

Principal = $ 160

So prize money at the end of year = 160*(1+0.05685)^145

= 160*(1.05685)^145

= 160*3033.444

= $ 485351.1

Part B

Future Value = Present value*(1+interest rate)^No. of years holding

(a) 196 = 170*(1+i)^3

196/170 = (1+i)^3

1.152941 = (1+i)^3

Take Cube Root(1/3) of both sides

1.048582 = 1+i

i = 1.048582 - 1

= 0.048582

= 4.86%

(b) 732/290 = (1+i)^17

2.524138 = (1+i)^17

take (1/17) of both sides

1.055975 = 1+i

i = 0.055975

= 5.60%

(c) 124723/32000 = (1+i)^18

3.897594 = (1+i)^18

take (1/18) of both sides

1.078505 = 1+i

i = 0.078505

= 7.85%

(d) 226140/31261 = (1+i)^20

7.233934 = (1+i)^20

take (1/20) of both sides

7.233934^(1/20) = 1+i

1.103999 = 1+i

i = 0.103999

= 10.40%

these roots can be solved over MS excel only.

Please check with your answer and let me know.