Investment
What is the present value of an annuity?
Annuity PV is today's value of equal payments at regular intervals discounted at one rate.
Definition
Annuity PV is today's value of equal payments at regular intervals discounted at one rate.
Intuition
Earlier payments have fewer discount periods; each due payment is one period earlier.
Formula
Annuity PV is payment times the annuity discount factor; for payments at period start, multiply by one period of growth. i is the periodic rate and n the payment count.
Variables and limits
PMT is the equal periodic payment, i is the nominal annual rate divided by frequency, and n is the payment count. Payments and discount periods must align; taxes, fees, and changing rates are excluded.
Example
- Enter a payment of 100, annual discount rate 10%, three payments, and annual frequency.
- End-of-period PV is 100/1.1 + 100/1.1² + 100/1.1³ ≈ 248.69.
- Beginning-of-period PV is about 273.55 after multiplying by 1.1; timing matters.
Common mistakes
Do not apply an annual rate directly to monthly payments; divide it by the number of payments per year.
Frequently asked questions
How do ordinary and due annuities differ?
An ordinary annuity pays at period end; an annuity due pays at period start, shifting every payment one period earlier.
What happens at a zero discount rate?
With no discounting, PV equals payment times number of payments for either timing.
Can payments vary?
Use NPV and discount each payment separately when amounts vary.