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

GROWING ANNUITY

It refers to a series of cash payments are received for a finite period of time and grows at propotional rate.

Example: A person receives $200 for the first year and the successive payments increase by 10% per year for a total of three years. There would be a receipt of $200, $220,$242 respectively.

GROWING PERPETUITY

It refers to a series of cah payments received for infinte period and at a propotional rate.

Example: Arun had invested in number of stocks in Reliance industries. At the end of first period he received a payment of $10000 which grows at a rate of 4% and continues forever. The discount rate is 10%.

Therefore the present value growing perpetuity is

PV = $10000/10%- 4% = $ 1,66,667.

ANNUITY TRANSFORMATION

It refers to an agreement between an individual and a firm where the individual pays a sum of amount once and receives in small lots regularly for a predetermined period. It is used to transform an ordinary annuity to annuity due.