Question

A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $ 1 comma 000. Each year after​ that, you will receive a payment on the anniversary of the last payment that is 5 % larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 15 % per year. a. What is​ today's value of the​ bequest? b. What is the value of the bequest immediately after the first payment is​ made?

a. What is​ today's value of the​ bequest? ​Today's value of the bequest is ​$

What is the value of the bequest immediately after the first payment is made?

Answer 1

First Payment = P = $1000

Interest Rate = 15% or 0.15

(a) PV = 1000/(1+0.15) + 1000*1.05/(1+0.15)² + 1000*1.05²/(1+0.15)³ + 1000*1.05³/(1+0.15)⁴ + ....

= 1000/(1+0.15) * ( 1 + 1.05/(1+0.15) + 1.05²/(1+0.15)² + 1.05³/(1+0.15)³ + .... )

= 1000/(1+0.15) * ( 1 / (1 - (1.05/1.15))) = $10000

(b) PV after first payment = 1000*1.05/(1+0.15) + 1000*1.05²/(1+0.15)² + 1000*1.05³/(1+0.15)³ + ....

= 1000*1.05/(1+0.15) * (1 + 1.05/(1+0.15) + 1.05²/(1+0.15)² + 1.05³/(1+0.15)³ + ....)

= 1000*1.05/(1+0.15) * ( 1 / (1 - (1.05/1.15))) = $10500