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vekshin1
3 years ago
14

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]
Business
1 answer:
DENIUS [597]3 years ago
8 0

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} ]

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