Annuity

An annuity is a finite stream of cash flows of identical magnitude and equal spacing in time.

E.g., Savings, vehicle, home mortgage, auto lease, bond payments

To compute the PV of an annuity, we could compute the PVs (at t=0) of the CFs individually and aggregate them, or we could use the formula below to directly compute the PV:

PV of Annuity = $CF * \frac{(1-(1+R)^{-T})}{R}$

where the term multiplied to CF is called the Annuity Factor.

This formula assumes that the first cash flow occurs at t=1. If the first cash flow occurs today i.e. at t=0, then we must add CF to the above formula.

Simple Example

How much do you have to save today to withdraw $100 at the end of each of the next 20 years if you can earn
5% per annum?

Here, CF=100, T=20, R=0.05

So, PV = $100 * \frac{(1-(1+0.05)^{-20})}{0.05}$ = $1246.22

Sidenote: A mortgage is an annuity where the borrowed amount is the present value of the annuity