Question

Joe lost his wife on New Year ’s Eve of 1970. When his wife died, Joe vowed to place fresh flowers on her grave every New Year ’s Eve as long as he lived. One year after his wife died, a bunch of fresh flowers costs about $10. Assume that the price of a bunch of flowers will grow at the rate of 3 percent annually and “Joe” could expect to live for 30 years after his wife died. If the annual interest rate is 6%, what is the present value of this commitment (year 1970)? Joe began purchasing flowers one year after his wife died.

Answer 1

Cost of Flower(C) =10
Number of Years =30
Rate =6%
PV of the commitment = C/(1+r) +C*(1+g)/(1+r)^2 +c*(1+g)^2/(1+r)^3.............+c*(1+g)^29/(1+r)^30
=10/(1+6%)+10*(1+3%)/(1+6%)^2+10*(1+3%)^2/(1+6%)^3.....................+10*(1+3%)^29/(1+6%)^30 =192.46

Alternate formula =C/(r-g)*(((1-(1+g)^n/(1+r)^n) =10/(6%-3%)*((1-(1+3%)^30/(1+6%)^30) =192.46