Question

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

Answer 1

An annuity is a stream of payments, at fixed intervals, during a given period of time. In case the amounts of periodical payments increase at a constant rate, on payment after payment, this annuity is called ‘growing annuity’. In the annuity, the payments cease on completion of the pre-determined period.

Example of growing annuity:

A savings plan in which the investor makes monthly deposits at the end of each month, for three years. First deposit will be of $1,000 on completion of one month from now and the amount will increase by 1% from the previous amount, month after month.

A growing perpetuity is a stream of payments, at fixed intervals, indefinitely, wherein the amounts of periodical payments increase at a constant rate, on payment after payment.

Example of growing perpetuity:

An endowment in which the beneficiary is paid at the end of each year, without stipulation of end-year. First payment will be of $1,000 on completion of one year from now and the amount will increase by 5% from the previous year, year after year.

Annuity transformation method by the process by which an ordinary annuity is converted into annuity due. Ordinary annuity is the annuity in which periodical payments are at the end of each period while in annuity due, payments are the beginning of the period. For transformation, first find out the present value or future value of the ordinary annuity and then multiply by (1+r) where r= interest rate.