Question

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

Answer 1

Formula for present value of growing annuity is:

PV = P/(r –g) [1 – (1+g/1+r)ⁿ]

P = Periodic cash flow = $ 2,500

r = Rate per period = 7.5 % or 0.075 p.a.

g = Growth rate = 5 % or 0.05

n = Numbers of periods = 20

PV = $ 2,500 / (0.075 – 0.05) x [1 – {(1+0.05)/ (1+0.075)}²⁰]

     = $ 2,500 / (0.075 – 0.05) x [1 – {(1.05)/ (1.075)} ²⁰]

     = ($ 2,500 /0.025) x (1 – 0.624621166)

     = $ 100,000 x 0.375378834

      = $ 37,537.88

Inheritance worth today is $ 37,537.88