Q.Find the present value of an annuity immediate of ₹18,000 per annum, for 3 years at 9% per annum, compounded annually.
[Given: $(1.09)^{-3} = 0.7722$]

By definition, an ordinary (immediate) annuity is one in which the equal payments or receipts occur at the end of each period; if they occurred at the beginning it would be an annuity due.

An annuity is a sequence of equal payments made at regular intervals. The classification depends on the timing of each payment within its period:

• Ordinary / immediate annuity — the payment is made at the end of each period (e.g. loan EMIs, most rent-type receipts recorded at period end).
• Annuity due — the payment is made at the beginning of each period. …

By definition, in an ordinary annuity each payment or receipt is made at the end of every period — option (b). (When payments are made at the beginning of each period it is called an annuity due.)

An annuity is a sequence of equal payments made at regular intervals of time. Annuities are classified by when within each period the payment occurs:

• Ordinary annuity (immediate annuity): each payment is made at the end of the period.
• Annuity due: each payment is made at the beginning of the period. …

A sequence of equal payments made at equal time intervals for a fixed (limited) number of periods is an annuity; only if it continued indefinitely would it be a perpetuity. Hence option (B).

Comparing the choices:

• Perpetuity — equal cash flows that continue for an unlimited (infinite) time, so it is ruled out by the word "limited period." …