Question

1) A rich relative has bequeathed you growing perpetuity. The first payment will occur in a year and will be $1,000. Each year after​ that, you will receive a payment on the anniversary of the last payment that is  7% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 13% 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?

Answer 1

1) PMT = 1,000

g = 7%

r = 13%

a) Today's value = PMT/(r - g)

Today's value = 1,000/(0.13 - 0.07)

Today's value = 1,000/0.06

Today's value = $16,666.6666666667

b) The value of the bequest immediately after the first payment is made = PMT * (1 + g)/(r - g)

The value of the bequest immediately after the first payment is made = 1,000 * (1 + 0.07)/(0.13 - 0.07)

The value of the bequest immediately after the first payment is made = 1,070/0.06

The value of the bequest immediately after the first payment is made = $17,833.3333333333