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. $X[a_{n} -v^{n} a_{m} ]$

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;

= $X * a_{n}$  - $Xv^{n} * a_{m}$

= $X[a_{n} -v^{n} a_{m} ]$