Present Value of Annuity Calculator
Calculate the present value of a series of equal periodic payments (annuity). This tells you how much a stream of future payments is worth in today's dollars, given a specific discount rate. Use this for retirement planning, loan valuation, or comparing investment options.
How to Calculate Present Value of an Annuity
- Determine the periodic payment amount (PMT) you will receive or pay.
- Identify the discount rate (interest rate) per period.
- Count the total number of payment periods.
- Apply the present value of annuity formula to find today's equivalent value.
- Compare the PV to the cost of purchasing the annuity or alternative investments.
Formula
PV = PMT × [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value of the annuity
PMT = Payment amount per period
r = Interest (discount) rate per period (as decimal)
n = Number of periodsExample
You will receive $1,000 per period for 10 periods at a 5% discount rate per period:
PMT = $1,000
r = 5% = 0.05
n = 10
PV = $1,000 × [(1 - (1.05)^-10) / 0.05]
= $1,000 × [(1 - 0.6139) / 0.05]
= $1,000 × [0.3861 / 0.05]
= $1,000 × 7.7217
= $7,721.73
The present value of receiving $1,000 per period for 10 periods at 5% is $7,721.73.Present Value of Annuity Reference Table
| PMT | 5%, 5 periods | 5%, 10 periods | 5%, 20 periods | 5%, 30 periods |
|---|---|---|---|---|
| $500 | $2164.74 | $3860.87 | $6231.11 | $7686.23 |
| $1,000 | $4329.48 | $7721.73 | $12462.21 | $15372.45 |
| $2,000 | $8658.95 | $15443.47 | $24924.42 | $30744.90 |
| $5,000 | $21647.38 | $38608.67 | $62311.05 | $76862.26 |
| $10,000 | $43294.77 | $77217.35 | $124622.10 | $153724.51 |
Present values at 5% discount rate per period
Frequently Asked Questions
What is the present value of an annuity?
The present value of an annuity is the current worth of a series of equal future payments, discounted at a specific interest rate. It answers: "How much would I need to invest today to generate these future payments?"
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity makes payments at the end of each period (like bond coupons), while an annuity due makes payments at the beginning (like rent). The PV of an annuity due equals the ordinary annuity PV multiplied by (1 + r).
What is the discount rate in annuity calculations?
The discount rate represents the time value of money — the return you could earn on an alternative investment of similar risk. A higher discount rate reduces the present value because future money is worth less today.
When should I use the present value of annuity formula?
Use it when evaluating lottery payouts (lump sum vs. annual payments), pricing bonds, valuing pension benefits, determining fair loan amounts, or comparing lease vs. buy decisions.
How does the number of periods affect present value?
More periods increase the present value because you receive more total payments. However, each additional payment contributes less due to discounting — payments far in the future are worth very little today.