Question

1. What is the present value of receiving $30 at the end of each year forever, starting 9 years from now? Assume an annual rate of interest of 7%

2. A perpetuity pays 1 at the beginning of every year. The present value is 10. Calculate the annual effective rate of interest earned by the perpetuity.

Answer 1

1. Amount= $ 30

Interest rate = 7 %

Present value of forever payment = Amount /i

= $ 30 / 0.07

= 428.57

PV of $30 starting 9 years from now = $ 428.57 / ( 1 + 0.07)^9 = 233.11

2.

Perpetuity pay = $ 1 at beginning of every year

Present vlaue = $ 10

Annual effective rate of interest = $ 1 / $ 10 = .10