Question

What is an annuity? Annuities due and ordinary annuities have a significant definitional difference. What is the difference? What is the difference between a perpetuity and an annuity?

Answer 1

Annuity is a system of equal, periodic payments received or to be made for a constant number of periods. It is widely used as a retirment product.

For example, Person A deposits $10,000 and buys a product, which starting next year would pay back A $1000 every year for 25 years. Or an example of interest payment - where equal monthly installments are to be paid to pack back a loan can also be seen as annuity

Annuities can be ordinary annuity or annuity due.

For ordinary annuity, the stream of periodic payments is expected to start next year (t=1) onwards, when we stand at current period (t=0).

Annuit due is also the stream of payments, but are expected to start from the currentyear (t=0) onwards itself.

This diagram well signifies the difference between the two:

Perpetuity is also a type of annuity, where there is a stream of periodic and equal paymenyts, however for infinite period of time. It is basically never-ending stream of payments (as opposed to annuity which has a defined end-point).