Question

6. [20] Your uncle is considering growing grapes in North Hidalgo County. He hopes to make 12% on his investment. The planting of the grape vines will cost him $20,000, and the grape vines take 4 years to mature (no grapes for the first four years). Then, the grape vines yield good grapes for 8 years. How much should the grape crops sell for each year for those eight years to make this investment viable?

Answer 1

future value of investment after 12 years

= 20000(1+i)^n

i = 12/100 ( assumed that interest compounded annually ) , n =12

= 20000( 1+0.12)^12

= 20000*3.89

= 77919

since 1st 4 years there is no revenue he has to get investment in 8 years

sales for year required ;

future value of annuity = 77919

n = 8

i = 12/100 = 0.12

future value of annuity = C((1+i)^n - 1) / i

77919 = C ( (1.12)^8 -1)/0.12

77919*0.12 = C ( 2.47-1)

C = 9350.28 / 1.47

= 6360.73

yearly sales required to earn 12% on his investment = 6360.73

note:

please provide feedback immediately to provide quality answers my correcting my self