Question

The PV of a 8 annual-payment growing annuity is $89,719.63. The first payment of the

growing annuity is $12,000 due one year from now. Subsequent annual payments are expected to

grow at an annual rate identical to the effective annual interest rate. What is the annual growth

rate?

Answer 1

Let annual interest Rate = r

Growth Rate = g

First Payment = P = $12000

Subsequent payments growth at rate g

Number of payments = n = 8

Hence, Present Value = PV = P/(1+r) + P(1+g)/(1+r)² + ..... P(1+g)⁷/(1+r)⁸

Given, PV = $89719.63 and g = r

=> PV = P/(1+g) + P(1+g)/(1+g)² + ..... P(1+g)⁷/(1+g)⁸
=> 89719.63 = P/(1+g) + P/(1+g) + ..... P/(1+g)
=> 89719.63 = 8P/(1+g)
=> 89719.63 = 8*12000/(1+g)
=> g = (8*12000)/89719.63 - 1 = 0.07 = 7%