Annuity Calculator: Future Value and Payment Amount

1. The rate you enter is a nominal yearly rate. It is divided by the number of payments in a year (monthly 12, quarterly 4, yearly 1) to get the rate for one period, r, and it compounds at the same frequency as the payments. For example, 5% compounded monthly is an effective yearly rate of about 5.12%. The site’s retirement withdrawal calculator converts a yearly return to an effective monthly rate instead, so the same input gives slightly different results there.
2. The number of payments, n, is the years times the payments per year.
3. For deposits: future value = starting amount x (1 + r)^n + deposit x ((1 + r)^n - 1) / r. For deposits at the start of each period, the deposit part is multiplied by (1 + r).
4. For a payment from a lump sum: payment = amount x r / (1 - (1 + r)^-n). For payments at the start of each period, divide that by (1 + r).
5. At a 0% rate, there is no growth: the future value is the starting amount plus deposit x n, and the payment is the amount divided by n.
6. Years are whole numbers from 1 to 100 and the rate can be from 0% to 30%. Results are in future dollars, not adjusted for inflation.

Check by hand, deposits: r = 0.06 / 12 = 0.005 and n = 240, so (1 + r)^n = 3.31020. The $10,000.00 grows to $33,102.04, the deposits add $300.00 x (3.31020 - 1) / 0.005 = $138,612.27, and together that is about $171,714.31. For the payment side, $100,000.00 at 5% a year, monthly for 20 years, has r = 0.05 / 12 = 0.0041667 and n = 240, so (1 + r)^-n = 0.36864 and the payment is about $100,000.00 x 0.0041667 / (1 - 0.36864), or $659.96 a month.

An ordinary annuity makes each payment at the end of the period, such as a deposit on the last day of the month. An annuity due makes it at the start. When paying out a lump sum, start-of-period payments are smaller, because each one comes a period sooner: $657.22 a month instead of $659.96 in the example above. When saving, start-of-period deposits earn one more period of interest each. With $10,000.00 to start, $300.00 a month, an assumed 6% and 20 years, the value is $171,714.31 with end-of-month deposits and $172,407.37 with start-of-month deposits.

With no interest the timing makes no difference. The same saver puts in $72,000.00 plus the starting $10,000.00 and ends with $82,000.00. In the interest-earning case, $89,714.31 of the $171,714.31 is interest from the rate you assumed.

The interest rate and the number of years are yours, and a contract may credit a different rate. A life annuity from an insurance company is priced from mortality tables and the insurer’s own terms, and it can include fees, a set pay period, tax treatment and other features that change the payment. This page does not model any of those, so use it to check the arithmetic and compare ideas, then read the actual terms. To see what a lump sum can pay over a set number of years, use the annuity payout calculator, which also handles a yearly increase and works backward from the payment you want.

To turn a balance into regular income, use the annuity payout calculator or the retirement withdrawal calculator. To project a workplace plan balance with an employer match, see the 401k calculator, and for required withdrawals from retirement accounts, the RMD calculator. For a savings account instead of a payout stream, try the high-yield savings calculator.