Question

An estate provides a perpetuity with payments of X at the end of each year. Seth, Susan, and Lori share the perpetuity such that Seth receives the payments of X for the first n years and Susan receives the payments of X for the next m years, after which Lori receives all the remaining payments of X. Which of the following represents the difference between the present value of Seth's and Susan's payments using a constant rate of interest?

a. X[an-vnam]
b. X[¨an-vn¨am]
c. X[an-vn+1am]
d. X[an-vn-1am]
e. X[van-vn+1am]

Answer 1

Answer: a.
`X[a_(n) -v^(n) a_(m) ]`

Step-by-step explanation:

The Present Value of the perpetuity for Seth is denoted by;

=
`X * a_(n)` because Seth receives it for n years.

The Present Value of the perpetuity for Susan is denoted by;

=
`Xv^(n) * a_(m)` because it is the value after n periods multiplied by the payments received for m periods.

The result is;

=
`X * a_(n)` -
`Xv^(n) * a_(m)`

=
`X[a_(n) -v^(n) a_(m) ]`