Mark has won a contest in which he will receive $10,000 at the end of each of the next 10 years and then $20,000 a year for the next 30 years after that. With an 8% discount rate, what is the present value of Mark's prize?

Question

Mark has won a contest in which he will receive $10,000 at the end of each of the next 10 years and then $20,000 a year for the next 30 years after that.  With an 8% discount rate, what is the present value of Mark's prize?

Reiny · Answer

PV = 10000(1 - 1.08)^-10)/.08 + 20000(1 - 1.08^-30)/.08 (1.08)^-10

= 171391.45

or

pretend you are gettting 20,000 for 40 years - the 10,000 for the first 10 years

= 20000(1 - 1.08^-40)/.08 - 10000(1 - 1.08^-10)/.08
= 171391.45