Annuity Calculator
What a stream of equal payments is worth today and what it adds up to at the end, paid at the start or the end of each period.
Results
What this tool does
An annuity is simply the same amount, paid over and over at regular intervals: a pension, a rent, a savings plan, a loan instalment. Two questions follow, and this page answers both. What is the whole stream worth right now, if you had to buy it or sell it today? And what will it have grown to by the time the last payment is made? Choose whether the money moves at the start or the end of each period — the difference is exactly one period's interest, and it is larger than most people expect.
Formula
PV = PMT × (1 − (1+i)^−n) ÷ i · FV = PMT × ((1+i)^n − 1) ÷ i · due: × (1+i)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pmt | Payment each period | — |
rate | Annual interest rate | % |
years | Years | — |
freq | Payments per year | — |
timing | When each payment lands | — |
target | Amount you want to reach | — |
PV | What the whole stream is worth today | — |
FV | What it adds up to at the end | — |
TP | Total paid | — |
IN | Interest earned | — |
DS | Taken off for waiting | — |
GP | Payment needed for that goal | — |
PR | Rate per period | % |
NP | Number of payments | — |
AF | Present value factor | — |
CF | Accumulation factor | — |
TM | Timing used | — |
Worked example
- Payment each period500
- Annual interest rate5 %
- Years10
- Payments per year12
- When each payment landsordinary
- Amount you want to reach0
- What the whole stream is worth today47,140.68
- What it adds up to at the end77,641.14
- Total paid60,000.00
- Interest earned17,641.14
- Taken off for waiting12,859.32
- Payment needed for that goal0.00
- Rate per period0.416667 %
- Number of payments120
- Present value factor94.281350
- Accumulation factor155.282279
- Timing usedEnd of period
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.
Frequently asked questions
What is the difference between the two timings?
Only when the money moves — but that one period changes everything by exactly one period's interest. Rent, insurance and most subscriptions are paid at the start: the landlord has your money for the whole month. Loan instalments, salaries and bond coupons come at the end. An annuity paid at the start is worth (1 + i) times one paid at the end, which at five per cent over ten years is a difference of about five per cent of the total. This page does both; pick the one that matches when the money actually leaves your hands.
Why is the value today so much less than the total?
Because the last payment is a long way off, and money that arrives in ten years is worth less than money in your hand now — not through inflation, but because the money you have now could be earning in the meantime. Ten yearly payments of 1,000 add up to 10,000, but at five per cent they are worth 7,722 today. The difference of 2,278 is what those ten years of waiting cost. That is also the honest way to compare a lump sum against an instalment offer: bring both to today.