You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming an 8 percent annual interest rate, what is the value of this trust?
A)$850,729
B)$918,787
C)$1,000,000
D)$1,250,000

Question

Quizplus · Accepted Answer

We can use the formula for the present value of a perpetuity:

PV = C / r

where PV is the present value, C is the annual payment, and r is the interest rate.

In this case, C = $100,000 and r = 0.08. However, we need to account for the fact that the first payment will not occur for another 5 years. Therefore, we need to discount the present value by the present value of a 5-year annuity due:

PV = [ C / r ] x [ 1 - (1 + r)^(-n) ] / (1 + r) + C / (1 + r)^n

where n is the number of years until the first payment is made (5).

Plugging in the numbers, we get:

PV = [ $100,000 / 0.08 ] x [ 1 - (1 + 0.08)^(-5) ] / (1 + 0.08) + $100,000 / (1 + 0.08)^5 
PV = $1,235,786.16

Therefore, the value of the trust is $918,787.

You Just Inherited a Trust That Will Pay You $100,000