Present Value of an Annuity
A level stream of end-of-period payments valued today. Solve for the present value, the payment that a present value supports, the implied rate, or how long a balance lasts.
PV of Ordinary Annuity (Annual Compounding)
Calculates the present value of a series of equal end-of-year payments.
When to use: Use to value a stream of future payments, like pricing a bond or valuing a lease.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PVA | Present Value of Annuity | Total present value of all payments | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Time period in years | years |
Real-Life Examples
Example 1: Lottery Winnings
A lottery pays $50,000/year for 20 years. At 8% discount rate, what is the lump-sum equivalent?
Given
Step-by-Step
For these inputs, Present Value of Annuity is $490,907.37 under the stated payment, compounding and accounting assumptions.
Example 2: Car Lease Valuation
A 5-year lease costs $4,800/year. At 6% discount rate, what is the total cost in present value?
Given
Step-by-Step
For these inputs, Present Value of Annuity is $20,219.35 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
The present value of an annuity is the current lump-sum equivalent of a series of future periodic payments. It tells you how much money you would need today to generate a specific stream of payments over time.
The present value formula determines the loan amount a series of payments can support. When a bank calculates how much you can borrow based on a payment you can afford, they are computing the present value of your payment stream.
Compare the lump-sum offer to the present value of the annuity payments using an appropriate discount rate. If the lump sum exceeds the present value, take the lump sum. If the present value is higher, the annuity payments are the better deal.
Use a rate that reflects your opportunity cost — the return you could earn on alternative investments of similar risk. Common choices include current market rates on government bonds (risk-free) or your expected portfolio return.
The calculator uses the finite zero-rate limit: an annuity’s value is payment times payment count; a solved payment is the target value divided by a positive payment count. Deferral has no effect at zero interest. Values require whole payment counts, even under continuous interest compounding.