# Annuity Calculator

> Find the future value and present value of a series of equal payments, paid at the start or end of each period, with an optional starting balance.

Category: Finance · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/annuity-calculator

An annuity is a series of equal payments at regular intervals. Its future value is what the payments grow to; its present value is what they are worth today.

Also called: Future value of annuity calculator, Present value of annuity calculator.

## Inputs
- Payment per period (default 500)
- Payments per year (options: Yearly, Half-yearly, Quarterly, Monthly; default 12)
- Interest rate (per year) (unit %; default 5)
- Years (default 20)
- Payments made at (options: End of period, Start of period; default end)
- Starting balance (default 0; optional)
- Currency

## Results
- Future value
- Present value (incl. starting balance)
- Present value of the payments
- Total payments
- Interest earned
- Number of payments

## Formula

```
FV = P(1 + i)^n + PMT × ((1 + i)^n − 1) ÷ i × (1 + i if paid at the start);  PV = PMT × (1 − (1 + i)^−n) ÷ i × (1 + i if paid at the start)
```

Where:
- PMT: payment per period
- i: annual rate ÷ payments per year
- n: years × payments per year
- P: starting balance

## Worked example
1. i = 5% ÷ 1 = 0.05; n = 10.
2. FV = 1,000 × (1.05^10 − 1) ÷ 0.05 = 1,000 × 12.5779 = 12,577.89.
3. PV = 1,000 × (1 − 1.05^−10) ÷ 0.05 = 1,000 × 7.7217 = 7,721.73.

**Result:** Ten yearly payments of $1,000 at 5% grow to $12,577.89; the same payments are worth $7,721.73 today.

## What the result means

Use the future value for saving towards a goal and the present value to price a stream of payments, such as a structured settlement or a lease. Payments at the start of each period (an annuity due) earn one extra period of interest, so both values are higher by a factor of (1 + i).

## Assumptions and limits
- The rate is constant and compounds once per payment period.
- All payments are the same size.
- Insurance-company annuity products have fees, surrender charges and guarantees that this calculation does not include.
- Taxes and inflation are not deducted.

## Questions

### What is the difference between an ordinary annuity and an annuity due?

An ordinary annuity pays at the end of each period (loan repayments, most bonds). An annuity due pays at the start (rent, insurance premiums). An annuity due is worth (1 + i) times more.

### Is this the same as an annuity I buy from an insurer?

The maths is the same, but a commercial annuity’s payout also depends on life expectancy, fees and the insurer’s pricing. Use the Annuity Payout Calculator to see what a balance can pay out.

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- [Annuity Payout Calculator](https://calculators.geekmidst.com/calculators/annuity-payout-calculator)
- [Compound Interest Calculator](https://calculators.geekmidst.com/calculators/compound-interest-calculator)
- [SIP Calculator](https://calculators.geekmidst.com/calculators/sip-calculator)
- [Pension Calculator](https://calculators.geekmidst.com/calculators/pension-calculator)

_Returns are illustrations at a constant rate, not predictions or guarantees. Investments can lose value. This is not investment advice._

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/annuity-calculator