This annuity calculator finds the level payment a lump sum can make each period until it runs out. At 6% a year, $100,000 pays $13,586.80 a year for 10 years.
It answers one of three annuity questions. The other two, present value and future value, have calculators of their own, linked further down.
One formula, three inputs
PV is the lump sum, i is the interest rate per period, and n is the number of periods. OpenStax defines an annuity as "a stream of fixed periodic payments to be paid or received in the future."
The calculator places each payment at the end of a period. Finance texts call that an ordinary annuity. The balance earns interest every period, so you're paid more in total than the lump sum.
Match the rate to the payment period
The rate field means the rate per period, not per year. For monthly payments, divide the annual rate by 12 and multiply the years by 12. Here's $100,000 at 6% a year over 10 years:
| How you enter it | Rate per period | Periods | Payment per period | Total paid out |
|---|---|---|---|---|
| Yearly payments | 6% | 10 | $13,586.80 | $135,868 |
| Monthly payments | 0.5% | 120 | $1,110.21 | $133,225 |
| Mixed up: yearly rate, monthly periods | 6% | 120 | $6,005.52 | $720,662 |
Monthly payments add up to $13,322.52 a year ($1,110.21 × 12), a little less than the yearly figure. Each payment leaves the pot sooner, so the balance earns less interest.
The third row is the classic mistake. It treats 6% as a monthly rate, which compounds to over 100% a year. The $6,005.52 it shows is meaningless.
Payments at the start of each period
An annuity due pays at the start of each period, so there's no wait for the first payment. Rent paid in advance works this way. OpenStax notes that an annuity due's present or future value is always larger, all else being equal.
This calculator can't switch timing, but the fix is one division. A due payment equals the ordinary payment ÷ (1 + i). For the yearly example, $13,586.80 ÷ 1.06 = $12,817.74.
That's smaller because the first payment leaves at once and never earns interest. Check which timing a quote uses before you compare two offers.
Where each payment comes from
Early payments are mostly interest. In the first year of the yearly example, the balance earns $6,000 ($100,000 × 6%). The other $7,586.80 of the payment comes out of your capital.
That split shifts every period. OpenStax explains the loan version: with fixed payments, the interest portion keeps falling and the principal portion keeps rising. Over 10 years you collect $135,868, so $35,868 of it is interest.
Why stretching the term stops helping
More periods lower the payment, but each extra decade does less. Here's $100,000 at 6% per period:
| Periods | Payment per period | Total paid out |
|---|---|---|
| 10 | $13,587 | $135,868 |
| 20 | $8,718 | $174,369 |
| 30 | $7,265 | $217,947 |
| 50 | $6,344 | $317,221 |
| 100 | $6,018 | $601,774 |
The payment can never fall below the interest alone: $100,000 × 6% = $6,000. At that level the lump sum is never touched and pays forever, which the perpetuity calculator values. Doubling from 50 to 100 periods barely moves the payment: $6,344 against $6,018.
Present value and future value: the other annuity questions
This page solves for the payment. Two related questions use the same ingredients:
- Present value: what a stream of equal payments is worth today. The present value of annuity calculator answers it.
- Future value: what equal deposits grow to by a later date. The future value of annuity calculator works that out.
The first is this calculator run in reverse. Enter $13,586.80 a period at 6% for 10 periods, and the present value comes back as $100,000.
Using it for an insurance annuity
The math assumes one fixed rate for the whole term. That suits a fixed contract, but not a variable annuity. The SEC's Investor.gov says a variable contract's value "will vary depending on the performance of the investment options you choose."
Fees matter too. Investor.gov warns that they "will reduce the value of your account and the return on your investment." So enter a rate after fees. For monthly income from a contract, the annuity payout calculator explains period-certain and lifetime payouts.