How the annuity calculator works
In finance, an annuity is any series of equal payments made at regular intervals. A savings plan where you put in $500 a month is an annuity. So is a pension that pays you $2,000 a month. Insurance companies also sell contracts called annuities, which use the same maths plus fees and guarantees.
The calculator covers both phases.
- Growth (accumulation). You pay in regularly, and the money earns interest. The result is the future value.
- Payout (income). You start with a lump sum and take regular payments while the rest keeps earning interest. You can find the payment for a set number of years, or how long a chosen payment lasts.
In both modes, the yearly rate is split evenly over the payment periods. At 5% with monthly payments, the rate per month is 5% ÷ 12 = 0.4167%, compounded monthly.
Payout payment: PMT = B × i ÷ (1 − (1 + i)^−n)
How long it lasts: n = −ln(1 − B × i ÷ PMT) ÷ ln(1 + i)
Annuity due (payments at the start of each period): multiply FV by (1 + i), divide PMT by (1 + i)
Here P is the starting amount, C the regular payment in, B the starting balance for a payout, i the rate per period and n the number of payments.
Ordinary annuity or annuity due?
The only difference is timing.
| Ordinary annuity | Annuity due | |
|---|---|---|
| Payments happen | At the end of each period | At the start of each period |
| Everyday examples | Loan payments, bond coupons | Rent, insurance premiums, many savings plans |
| Effect when saving | Lower future value | Higher future value (× (1 + i)) |
| Effect when drawing income | Higher payment | Slightly lower payment (÷ (1 + i)) |
When saving, an annuity due is worth more, because each payment earns one extra period of interest. When drawing income, paying at the start of each month means the money earns a little less, so each payment is slightly smaller.
Worked example 1: saving for 20 years
These are the calculator’s starting numbers. You put $50,000 into an account earning 5% a year and add $500 at the end of every month for 20 years.
- Rate per month: 5% ÷ 12 = 0.41667%. Number of payments: 240.
- The $50,000 grows to $50,000 × 1.0041667^240 = $135,632.01.
- The $500 payments grow to $500 × (1.0041667^240 − 1) ÷ 0.0041667 = $205,516.83.
- Future value: $341,148.85. You paid in $170,000, and interest added $171,148.85.
If you then draw that balance down over 20 years at the same 5%, it pays about $2,251.43 a month.
Worked example 2: income from a lump sum
You retire with $500,000 and want it to last 25 years. The money keeps earning 5% a year, and you take a payment at the end of each month.
- Payment: $500,000 × 0.0041667 ÷ (1 − 1.0041667^−300) = $2,922.95 a month.
- Over 25 years you receive $876,885. That is your $500,000 plus about $376,885 of interest earned along the way.
- If you take each payment at the start of the month instead, it falls to $2,910.82.
This is the same maths as a 25-year loan of $500,000 at 5%: the bank’s monthly payment would also be $2,922.95. Paying yourself an income is a loan in reverse.
Worked example 3: how long will the money last?
Same $500,000 at 5%, but you want $3,000 a month.
- n = −ln(1 − 500,000 × 0.0041667 ÷ 3,000) ÷ ln(1.0041667) = 285.1 months.
- You get 285 full payments and a smaller final one, about 23 years 10 months in total.
Lower the payment to $2,083.33 a month or less and the money never runs out, because the interest alone covers it. That is the “interest-only” payment the calculator shows.
Annuities you can buy
Insurance companies sell several kinds of annuity contract. The US Securities and Exchange Commission’s Investor.gov explains the main types.
- Fixed annuities pay a guaranteed minimum interest rate while your money grows. The payout can be for a set period or for life.
- Variable annuities invest your money in sub-accounts, usually mutual funds, so the value rises and falls with the markets. They are securities regulated by the SEC.
- Indexed annuities link returns to a market index such as the S&P 500, usually with a cap on gains and a floor on losses.
- Immediate annuities start paying right after you buy them. Deferred annuities grow first and pay later.
Contracts often add costs this calculator does not include. These can be mortality and expense charges, administrative fees, fund expenses, fees for optional riders, and surrender charges if you take money out early. To allow for fees, enter a lower rate.
Tips
- Test a range of rates. A 1% change in the rate changes a 25-year income by about 10%.
- Think about inflation. A fixed $2,923 a month buys less every year. At 2.5% inflation it buys about half as much after 28 years.
- Compare with Social Security. Waiting to claim Social Security raises a lifetime, inflation-adjusted payment by 8% a year after full retirement age. See the Social Security calculator.
- Check the whole plan. The retirement calculator shows how savings, withdrawals and inflation work together. The compound interest calculator handles other compounding frequencies.
- Remember required withdrawals. Money in a traditional IRA must start coming out at 73 or 75. The RMD calculator shows how much.
This calculator shows the time-value-of-money maths at a fixed rate. It is for education, not financial advice. Read any annuity contract and its prospectus, and compare quotes, before you buy.