Present Value of an Annuity in 9 Minutes
An annuity is a series of equal payments made at regular intervals for a set number of periods, like loan payments or rent. Instead of discounting each payment one by one, the present value of annuity formula does it all in one step.
What you will learn
- What an ordinary annuity is
- The present value of annuity formula and the annuity factor
- How to value loan payments, leases and other equal cash flows
- How annuities relate to perpetuities
The formula
- C
- equal payment at the end of each period
- r
- discount rate per period
- n
- number of payments
Worked example
You will receive $1,000 at the end of each year for 5 years. The discount rate is 6%. What is the stream worth today?
- Inputs: C = $1,000, r = 0.06, n = 5.
- Discount the last payment's factor: (1.06)⁻⁵ ≈ 0.747258.
- Annuity factor: (1 − 0.747258) ÷ 0.06 ≈ 4.212364.
- PV = $1,000 × 4.212364 ≈ $4,212.36.
Answer: About $4,212.36 today (rounded to the cent).
Common questions
What is the formula for the present value of an annuity?
PV = C × [1 − (1 + r)⁻ⁿ] ÷ r, where C is the payment per period, r is the rate per period and n is the number of payments. This version assumes payments come at the end of each period.
What is an annuity factor?
The annuity factor is the [1 − (1 + r)⁻ⁿ] ÷ r part of the formula. It tells you what $1 a period for n periods is worth today. At 6% for 5 years it is about 4.2124.
What is the difference between an annuity and a perpetuity?
An annuity pays for a fixed number of periods, while a perpetuity pays forever. In fact, an annuity's value equals a perpetuity with its first payment in period 1 minus a perpetuity with its first payment in period n + 1.
How do you calculate the present value of an annuity on a financial calculator?
Enter N as the number of payments, I/Y as the rate per period, PMT as the payment and FV as 0, then compute PV. The answer shows as negative on many calculators because it is treated as a cash outflow.