Annuity — Meaning and Types

A single deposit growing under compound interest, studied earlier in this course, answers 'what does one lump sum become after $n$ years?' Many real financial commitments — a monthly salary saved into a recurring deposit, a home-loan EMI, a pension paid every year after retirement — instead involve a series of equal payments made at regular intervals. This series is called an annuity, and this chapter builds the two formulas needed to value it: its future value (what the series grows to) and its present value (what the series is worth today).

Two types of annuity are distinguished by when in each period the payment falls:

• Annuity Immediate (Ordinary Annuity): each instalment is paid at the end of every period. This is the more common case in practice — a loan EMI, a recurring deposit's monthly instalment, and an insurance premium are all typically paid at period-end.
• Annuity Due: each instalment is paid at the beginning of every period. Because every payment in an annuity due sits one full period earlier than the corresponding payment in an otherwise identical ordinary annuity, every value connected with an annuity due is always exactly $(1+i)$ times the corresponding ordinary-annuity value, where $i$ is the interest rate per period — a useful relationship for converting between the two without re-deriving a separate formula from scratch.

This distinction — end-of-period versus beginning-of-period payments — and the resulting family of annuity formulas is a standard, board-independent piece of financial mathematics, taught identically (using the same instalment/interest-rate/time framework) wherever compound-interest-based savings and loan calculations are covered in Indian commerce mathematics.