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Formula sheet/NISM Series X-A: Investment Adviser (Level 1)/Personal Financial Planning
[ PERSONAL FINANCIAL PLANNING ]

Ordinary Annuity, Annuity Due, and Perpetuity

Ordinary Annuity PV:PV=C×[1−(1+r)−n/r](Payments at end of period,Excel type=0)\text{Ordinary Annuity PV}: PV = C \times [ { 1 - (1 + r)^{-n} } / r ] (\text{Payments at end of period}, \text{Excel type}=0)
Annuity Due PV:PVdue=PVordinary×(1+r)(Payments at beginning of period,Excel type=1)\text{Annuity Due PV}: PV_{\text{due}} = PV_{\text{ordinary}} \times (1 + r) (\text{Payments at beginning of period}, \text{Excel type}=1)
Perpetuity PV:PV=C/r(Constant perpetual cash flow stream)\text{Perpetuity PV}: PV = C / r (\text{Constant perpetual cash flow stream})
Variables

C: Periodic cash flow; r: Periodic discount rate; n: Number of payment periods.

Exam note

Annuity due is worth more than ordinary annuity because each cash flow is received one period earlier, compounding extra returns.

Worked example
Annuity Due vs. Ordinary Annuity Cash Flow Valuation

A landlord leases commercial property for 5 years at an annual rent of Rs 12,00,000. Rent is payable annually in advance (at the beginning of each year). If the discount rate is 9.0% p.a., calculate the Present Value of the rental income stream (Annuity Due) and compare it with an Ordinary Annuity.