What is Perpetuity and Annuity? Comparison Chart and Free Calculator
If you're learning more about investing, or simply moving closer to retirement the way all of us eventually do, perpetuity and annuity are two terms worth actually understanding rather than glossing over. They sound similar, show up in a lot of the same conversations about fixed income, and are genuinely easy to mix up.
The short version: a perpetuity is a stream of equal payments that never ends, while an annuity is a stream of equal payments that runs for a fixed, defined period and then stops. That single distinction, payments forever versus payments for a set term, drives almost every other difference between them. This guide breaks both down across nine key areas, walks through how to calculate each one with real worked examples, and gives you two free interactive calculators to run your own numbers.
Comparison of Perpetuity and Annuity Across 9 Areas
| Area | Perpetuity | Annuity |
|---|---|---|
| Definition | A stream of equal payments that continues forever | A stream of equal payments made over a fixed, defined term |
| Duration | Infinite, with no end date | Finite, payments stop after a set number of periods |
| Present value formula | PV = Payment ÷ Discount Rate | PV = Payment × [(1 − (1+r)⁻ⁿ) ÷ r] |
| Payment stream | Same payment, paid indefinitely | Same payment, paid for a defined number of periods |
| Common examples | Certain preferred stock dividends, some perpetual bonds, terminal value in valuation models | Retirement annuities, structured settlements, loan and mortgage payments |
| Typical use case | Valuing assets whose cash flows are assumed to continue indefinitely | Retirement income planning, structured payouts, loan amortization |
| Risk profile | Value is sensitive to interest rate changes indefinitely, with no maturity to anchor it | Interest rate risk is bounded by the fixed term length |
| Liquidity | Tradable if the underlying instrument has a secondary market (e.g. a bond or preferred share) | Often less liquid early on due to surrender periods or withdrawal penalties |
| Tax treatment | Depends entirely on the specific instrument generating the payments | Most commercial annuities grow tax-deferred and are taxed as ordinary income on withdrawal |
How to Calculate a Perpetuity
The present value of a perpetuity is one of the simplest formulas in finance, precisely because there's no end date to account for:
Let's use an example of a bond that pays for an infinite time. The bond pays $200 every year and the discount rate is 5%.
PV = $4,000
If you have a bond that pays $200 each year infinitely at a 5% discount rate, the present value of that perpetuity is $4,000, which would be the fair price of the bond today.
💰 Perpetuity Calculator
Enter a payment and discount rate to calculate present value instantly.
Why Would You Purchase an Annuity?
An annuity isn't the right fit for everyone, but it's a reasonable choice for a fairly specific set of people. It tends to appeal to anyone who finds the stock market's swings too unpredictable for their comfort, wants to know in advance roughly how much interest they'll earn rather than hoping for the best, or values the certainty of a predictable income stream over the higher but less certain returns the market might offer. It can also make sense for someone who doesn't qualify for life insurance, or who is specifically worried about long-term care costs and wants a structured way to cover them.
How to Calculate an Annuity
Annuity math is more involved than perpetuity math because a fixed end date has to be built into the formula:
Let's use an example of someone who is likely to purchase an annuity. They want to move $20,000 into an annuity with a 0.5% monthly interest rate for 10 years (120 months). We'll solve for the value of each monthly payment.
P ≈ $222.04
Now compare $20,000 going in against $222.04 paid out every month for 120 months, which totals roughly $26,644.92. By purchasing the annuity, you come out about $6,644.92 ahead over 10 years. That's potentially safer than stocks, but at that interest rate, you may have done little more than keep pace with inflation. Even so, it's a better outcome than letting the money sit completely idle.
💰 Annuity Payment Calculator
Enter a present value, periodic rate, and number of periods to calculate the payment per period.
Frequently Asked Questions About Perpetuity and Annuity
Final Takeaway
When you hear the terms perpetuity and annuity, you should be comfortable knowing the core difference between them, payments forever versus payments for a fixed term, and what it looks like to quickly calculate either one. Use the calculators above any time you need real numbers rather than rough estimates.