Annuity Calculator
Work out what regular payments grow to, the income a lump sum can pay, or what a stream of payments is worth today.
A growing annuity, e.g. to keep up with inflation.
Shows results in today's money too.
Year-by-year balance and chart
| Year | Start | Paid in | Interest | End | End, today's money |
|---|
How your annuity is worked out
Turn the yearly rate into a rate per payment, count the payments, then add up what each one is worth.
- 1
Rate per month
6% ÷ 12= 0.5%
- 2
Count the payments
20 yrs × 12= 240 payments
- 3
Annuity factor
(1.005^240 − 1)÷ 0.005= 462.04
- 4
Your future value
500 × 462.04+ 10,000 grown= 264,122
Read more: the formulas, a worked example and annuity due vs ordinary
An annuity is any series of equal (or steadily rising) payments made at regular times: saving a fixed amount each month, a pension or insurance annuity that pays you an income, loan repayments or rent. This calculator does the pure time-value-of-money maths for all three questions people ask about them. It does not include any insurer's fees, charges, mortality pooling or tax, so an annuity quote from a provider can differ. For a mutual fund income plan see the SWP calculator, and for savings that grow see the compound interest calculator.
The formula
rate per payment i = (1 + yearly rate ÷ m)^(m ÷ q) − 1
future value = S × (1 + i)^n + P × ((1 + i)^n − 1) ÷ i
present value = P × (1 − (1 + i)^−n) ÷ i
payment from a lump sum L = L × i ÷ (1 − (1 + i)^−n)
annuity due (paid at the start): multiply the value by (1 + i), or divide the payment by (1 + i)
Here P is the payment, n the number of payments, q the payments a year and m how many times a year interest is compounded (when m = q, i is just the yearly rate ÷ q). S is a starting balance. With continuous compounding, i = e^(yearly rate ÷ q) − 1.
growing annuity (yearly payments) = P ÷ (r − g) × (1 − ((1 + g) ÷ (1 + r))^n)
when g = r: n × P ÷ (1 + r)
perpetuity = P ÷ i, growing perpetuity = P ÷ (r − g)
how long a lump sum lasts: n = −ln(1 − L × i ÷ P) ÷ ln(1 + i)
Here g is the yearly rise in the payment. With monthly payments that rise once a year, the calculator values each payment one by one, which gives the exact answer for any g, including g equal to the rate.
Worked example
10,000 to start plus 500 at the end of every month, at 6% a year compounded monthly, for 20 years: i = 0.06 ÷ 12 = 0.005 and n = 20 × 12 = 240, so (1.005)240 = 3.310204.
- The starting balance grows to 10,000 × 3.310204 = 33,102.04.
- The annuity factor is (3.310204 − 1) ÷ 0.005 = 462.0409, so the payments grow to 500 × 462.0409 = 231,020.45.
- Future value = 33,102.04 + 231,020.45 = 264,122.49.
- You pay in 10,000 + 500 × 240 = 130,000, so the interest is 264,122.49 − 130,000 = 134,122.49.
- Paid at the start of each month instead (annuity due), the payments grow to 231,020.45 × 1.005 = 232,175.55, so the total is 265,277.59.
Turning it round: 300,000 paid out monthly over 20 years at 5% gives i = 0.05 ÷ 12 = 0.0041667, (1.0041667)−240 = 0.368633, so the payment is 300,000 × 0.0041667 ÷ (1 − 0.368633) = 1,979.87 a month. And 1,000 a month for 20 years at 5% is worth 1,000 × (1 − 0.368633) ÷ 0.0041667 = 151,525.31 today.
Which goal to pick
| You want to know | Pick | Example |
|---|---|---|
| What regular saving adds up to | What savings grow to | 500 a month for 20 years |
| The income a pot of money can pay | Income from a lump sum → The payment | 300,000 at retirement |
| How long an income will last | Income from a lump sum → How long it lasts | 2,000 a month from 300,000 |
| The fair price of an income, or a lump sum vs payments choice | What payments are worth today | A lottery or pension buyout |
In the example, 2,000 a month from 300,000 at 5% lasts 235 full payments (19 years 7 months) plus a smaller last one, because 2,000 is more than the 1,250 a month the money earns. Take 1,250 or less and it never runs out.
Returns and annuity rates are not guaranteed. Real annuities from insurers include charges, may pay for life rather than a fixed term, and are taxed under your country's rules, none of which are included here. This is an illustration, not financial advice.
Common questions
How is the future value of an annuity worked out?
Each payment grows at the interest rate for the time it has left, and the starting balance grows for the whole time. 10,000 plus 500 at the end of every month at 6% a year for 20 years grows to about 264,122. You pay in 130,000, so about 134,122 is interest.
How much income will a lump sum pay each month?
300,000 at 5% a year, paid out over 20 years, gives about 1,979.87 a month if each payment is at the end of the month, or 1,971.65 if paid at the start. To keep the 300,000 whole and pay out only the interest, you could take 1,250 a month for ever.
What is the difference between an annuity due and an ordinary annuity?
In an ordinary annuity each payment is at the end of the period; in an annuity due it is at the start. Paying in earlier means each payment earns one extra period of interest, so the future value is (1 + i) times higher: 264,122.49 becomes 265,277.59 in the example.
What is the present value of an annuity?
It is the lump sum today that is worth the same as a stream of payments, because money now can earn interest. 1,000 a month for 20 years adds up to 240,000, but at 5% a year it is worth about 151,525 today. That is also the lump sum you would need to pay yourself 1,000 a month for 20 years.
What are a growing annuity and a perpetuity?
A growing annuity's payments rise each year, for example with inflation. 10,000 a year rising 3% a year, for 25 years at 7%, is worth about 153,556 today. A perpetuity pays for ever: it is worth the payment ÷ (rate − growth), so 10,000 a year rising 3% at 7% is worth 250,000.
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