Question

Jade has an investment worth $80,000. The investment will make a special extra payment of X to Jade in 3 years from today. The invesmtne will also make regular, fixed annual payments of $12,400 to Jade with the first of these payment made to Jade later today and the last of these annual payments made to Jade in 5 years from Today. The expected return for the investment is 8.5% per year. What is x , the amount of the special payment that will be made to Jade in 3 years?

A greater than or equal to $10,000 but less than $15,000

B greater than or equal to $15,00 but less than $20,000

C greater than or equal to $25,000 but less than$31,000

D greater than or equal to $20,000 but less than $25,000

E none

Answer 1

First we have to calculate present value of all 12,400 Payments on today

Presenet value of annuity Due = P*[1 - (1+r)^-n / r ]*(1+r)

= 12400*[1 - (1+8.5%)^-6 / 8.5%]*(1+8.5%)

= 61,263.96

Balance = 80,000 - 61,263.96 = 18,736.04

so Presennt value of 'X' should be 18,736.04

Present value = Future value / (1+8.5%)^3

18,736.04 = X / 1.27728

so X = 23,931.34

So Option D is correct