Question

At an annual effective interest rate i > 0, all three of the following are equivalent (equal present value).

(1) a payment of 20,000 four years from now
(2) a payment of 11,000 t years from now and 11,000 2t years from now

(3) 12,000 immediately

What is the present value of a payment of 15,000 made t+2 years from now?

Answer 1

At effective interest rate i, present value of all options are equal

(3) pays 12000 immediately. Its present value in all cases would be $12000

Present value of all options are equal, so present value of $20000 received in 4 years = 12000

Present value = 12000

future value = 20000

number of years (n) =4

FV/(1+i)^n = PV

20000/(1+i)^4 = 12000

(1+i)^4 = 20000/12000

1+i = (1.666666667)^(1/4)

i =1.136219367-1

i=0.136219367

So annual effective interest rate =.136219367

payment received after 2 years = 15000

number of years (n) =2

Present value = future value/(1+i)^n

=15000/(1+.136219367)^2

=11618.95003

So present value of $15000 receied in T+2 years is $11618.95