A certain investment promises to pay you $2,500 per year forever with the first payment starting 5 years from now.If you can earn a 5% return on similar investments,what's the most you would pay for this investment today?
A)$50,000
B)$39,176
C)$41,135
D)$37,311

Question

Quizplus · Accepted Answer

Using the formula for the present value of perpetuity:
PV = C/r, where PV is the present value, C is the cash flow (in this case, $2,500), and r is the discount rate (in this case, 5% or 0.05).
PV = $2,500/0.05 = $50,000
However, since the first payment will start 5 years from now, we need to discount the present value by the present value of $2,500 for 5 years at 5%:
PV = [ $2,500 / (0.05) ] * [ 1 - (1/ (1.05)^5) ]
PV = $41,135.25
Therefore, the most you should pay for this investment today is $41,135.25, which is answer choice C.

A Certain Investment Promises to Pay You $2,500 Per Year