Question

Discuss the difference between a growing annuity and a growing perpetuity. Provide an example of each. Also explain the annuity transformation method.

Answer 1

In a growing annuity, a series of cash flows are accumulated at a proportionate rate upto a fixed finite period of time. In growing perpetuity, a series of cash flows are accumulated at a proportionate rate but the period of time is infinite and perpetual in nature.

A annuity transformation method is a method by which the present value of annuity payment outflows can be transformed to multiple and equal installments of smaller inflows. Thus if I pay X today to receive x1 for 10 years, this is done using annuity transformation method. This is especially used in annuity purchases for Inrance sector. If a person calculates his monthly expense after retirement to be 5K and as per calculation, he is assuming to live for 20 years l, he can purchase a annuity by paying the present value of 5I monthly for 20 years at the prevalent interest rate. This is a practical use of annuity transformation method.