411.2
2.Let's say that you have 2 grandchildren and you want to give
them something to remember you by when you die. You want to set
up a fund that will pay each of them $1000 per year forever
starting when they turn 18. If one of your grandchildren is 17
and the other is 14, what total amount do you need to invest
today? Assume a discount rate of 8% per year.
There are two perpetuities here: a regular one and a deferred one. For the grandchild that turns 18 next year, this is a regular perpetuity and its PV today (when he is 17) is just: 1000/.08=$12500.
17 18 19 20 … 1000 … 1000 … 1000 … For the child that turns 18 in 4 years, this is a deferred perpetuity:
14 15 16 17 18 19 … 0 0 0 1000 1000 … We know that the value of this perpetuity will be $12500 when the child is 17. Thus, today, when he or she is 14, the value is $12500/(1.08)^3 = $9922.90
The total cost of the 2 perpetuities is $12500+$9922.90=$22422.90.