Question

1. For a given n, PMT and i, is the present value of a deferred annuity the same as the present value of an ordinary annuity?
2. Does a portability clause in the mortgage agreement mean that a purchaser may acquire the existing mortgage? In a deferred annuity, is the original value or the future value used to calculate payments that commence at the end of the deferral period?

Answer 1

a) No, given all terms being the same the present value of a deferred annuity will not be the same as the present value of an ordinary annuity for the reason explained below.

In a deferred annuity, you can contribute one or more cash payments up to a future date, called the annuity date, when you stop contributing and begin receiving your payments. An example of a deferred annuity would be to contribute $10,000 into an annuity account with a fixed interest rate of 9.6 percent annual, (0.8 percent monthly) and then, in three years, start receiving monthly payments of $93.87 for the following 20 years. Each succeeding payment is worth less in today's dollars than the one before it because of the time value of money.

b) Yes, it means that a pruchaser may acquire the existing mortgage.

c) Future value is used to calculate payments as we are trying to arrive at the amount that needs to be invested today to achieve a specific income target.