Annuity table
A pre-computed table that gives the present-value multiple, or annuity factor, for a given interest rate and number of years, letting you value a regular cash flow without solving the formula each time.
In plain language
Valuing an annuity — a regular payment repeated every year — means working out the present value of every single payment and adding them up, or using the present value formula. That is not always convenient to do by hand.
An annuity table does the work in advance. Look up the row for the interest rate you need and the column for the number of years, and the table gives you a single number called the annuity factor. Multiply the yearly payment by this factor, and you have the present value — no formula needed.
How it works
The annuity factor from the table is the same number the present value formula would produce for an annuity of Rs 1 a year, at a given rate for a given number of years. To value any regular annual payment, multiply it by the factor.
The workbook's own example looks up the factor for 10 years at 5% per annum, which the table gives as 7.7217. Multiplying by an annuity of Rs 12,000 a year gives the present value directly, without touching the underlying formula at all.
The formula
PV = Payment x Annuity factor(r, n)
Annuity factor(r, n) = (1 - (1/(1+r)^n)) / r
The annuity table simply stores this factor pre-calculated for common combinations of r and n.
A worked example
A person wants to value an annuity of Rs 12,000 a year for 10 years at 5% per annum.
Using the full present value formula:
PV = 12,000 x ((1 - (1/(1.05)^10)) / 0.05) = Rs 92,660
Using the annuity table instead: look up the factor for 10 years at 5%, which is 7.7217.
PV = 12,000 x 7.7217 = Rs 92,660
Both routes give the identical answer, Rs 92,660 — the annuity table is simply a shortcut to the same present value calculation.
Why NISM asks about it
Chapter 2 (Time Value of Money), section 2.2.6 'Annuity', introduces the annuity table right after showing the present-value formula for an ordinary annuity, and works the Rs 12,000-a-year, 10-year, 5% example both ways. Expect a question that gives you an annuity factor directly and asks you to multiply it by a cash flow, or one that expects you to recognise the table result should match the formula result.
Common exam traps
- An annuity table factor is built for an ordinary annuity (payment at the end of each period) unless stated otherwise. An annuity due, paid at the start of each period, is worth more and needs an adjustment.
- The table gives a present value factor, not a future value factor — do not use it to project a cash flow forward.
- Always match the table's rate and period to the cash flow's own frequency: an annual table factor cannot be applied directly to a monthly annuity.
Where this is taught
Free preparation for NISM Series X-ARelated terms
- PerpetuityA constant cash flow received every period with no end date. Its present value is simply the cash flow divided by the discount rate: PV = C / r.
- Annuity dueAn annuity whose payments fall at the beginning of each period rather than the end, which makes it worth more than an otherwise identical ordinary annuity.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.
- Ordinary annuityA series of equal payments falling at the end of each period — the default form of annuity, and the one every standard present value and EMI calculation assumes.
- Compound interest rateThe rate at which a present sum of money grows into the future once its interest is reinvested and starts earning interest of its own, the forward-looking twin of the discount rate.
- Compounding periodThe interval, such as monthly, quarterly or annually, over which interest is calculated and added to an investment — the more often it happens within a year, the faster the investment grows.
- Fixed annuityAn annuity that pays a fixed, unchanging amount at each regular period, agreed at the time of investing — as against a floating annuity, whose payouts move with an inflation or index benchmark.
- Floating annuityAn annuity whose payout is not fixed but moves with a chosen benchmark — inflation, an index, or another agreed return — decided when the investment is made, as against a fixed annuity.