Question

Given an interest rate of 6.5 percent per year, what is the value at year 10 of a perpetual stream of $3500 payments that begin at year 20?

Answer 1

First we need to calculate the PV of the perpetuity at the beginning of year 20, then we need to discount it for 9 years to calculate the PV at the beginning of year 10

We are given the following information:

Annual payment	PMT	$       3,500.00
rate of interest	r	6.50%
number of years	n	10
Future value	PV20	To be calculated

We need to solve the following equation to arrive at the required PV20

So the PV20 is $25160.91

Now we discount it back for 9 years to calcualte PV10

We are given the following information:

Value of account at time 0	PV10	To be calculated
rate of interest	r	6.50%
number of years	n	9
Future value	PV20	$     25,160.91

We need to solve the following equation to arrive at the required PV10

So the PV at the beginning of year 10 is 14538.58