What this calculator computes
This is an accumulation calculator for the future value of an ordinary annuity: a fixed contribution paid at the end of every month, growing at a fixed rate, for a set number of years, optionally on top of a starting balance. It answers what a savings or investment plan is worth at the end, not what income a commercial annuity product would pay you.
The formula has two parts. The contribution stream uses FV equals PMT times ((1 plus r) to the power of n, minus 1), divided by r, where PMT is the monthly contribution, r is the monthly rate, and n is the number of months. The starting balance uses FV equals starting balance times (1 plus r) to the power of n. The two are added.
The monthly rate is the annual rate divided by 12, and the number of periods is years times 12, rounded to a whole number of months. When the rate is zero, the contribution term reduces to PMT times n, which is simply the sum of the deposits.
A worked example: 500 a month for 20 years at 6 percent
The monthly rate is 6 percent divided by 12, or 0.5 percent, which is 0.005 as a decimal. The number of months is 20 times 12, or 240. The growth factor 1.005 to the power of 240 is about 3.3102.
The contribution term is 500 times ((3.3102 minus 1) divided by 0.005), which is 500 times about 462.04, or roughly 231,020. With a starting balance of zero, that is the whole future value.
Total contributions are 500 times 240, or 120,000. Interest earned is 231,020 minus 120,000, or about 111,020, slightly more than the contributions themselves. If you had also started with 10,000, that lump sum would grow to 10,000 times 3.3102, or about 33,102, bringing the total to roughly 264,122 against 130,000 contributed.
Ordinary annuity versus annuity due
This tool uses the ordinary annuity convention, meaning each payment lands at the end of its month. An annuity due, where payments are made at the start of each period, gives every contribution one additional month of growth. The relationship is simple: the annuity due value is the ordinary annuity value multiplied by one plus the monthly rate.
In the worked example, that factor is 1.005, so a start-of-month schedule would produce about 232,175 rather than 231,020, a difference of roughly 1,155 over twenty years. The gap is small relative to the total but grows with the rate and the horizon.
If your real deposits land on the first of the month, multiplying the result by one plus the monthly rate gives the correct figure. For most planning purposes the difference is inside the noise created by the other assumptions.
Accumulation annuities versus income annuities
The word annuity covers two distinct things. In the mathematical sense it means any series of equal payments at regular intervals, which is what this calculator handles. In the insurance sense it means a contract where you hand over a sum in exchange for a guaranteed stream of payments, often for life.
This tool does not model an insurance annuity product. It does not account for the insurer's fees and expense charges, surrender periods and penalties, mortality credits, guaranteed minimum rates, riders, or the payout factor used to convert a balance into lifetime income. The output is the accumulated value of a savings plan, which is one input to a decision about such a product, not a quote for one.
It also does not model the decumulation phase. Working out how long a balance lasts under regular withdrawals, or what withdrawal rate a balance supports, is a different calculation that involves sequence of returns and longevity, neither of which appear here.
Assumptions that limit the result
The rate is constant for the entire term. Real returns vary, and for a market-linked plan the sequence of returns matters, particularly when you are contributing steadily: a poor early period followed by a strong late one produces a different outcome than the reverse, even at the same average. A constant rate gives you a clean comparison point rather than a forecast.
Contributions are constant too, with no escalation for inflation or pay rises, and no allowance for missed months. Over twenty years a fixed 500 a month is a shrinking real contribution, so a plan that keeps pace with inflation would end up ahead of the figure shown while contributing more in nominal terms.
The result is nominal and pre-tax, and it excludes fees. To make it more realistic, deduct expected annual fees from the rate before entering it, and consider entering a rate net of expected inflation if you want the answer in today's purchasing power. At 6 percent nominal with 2.5 percent inflation, entering 3.5 percent instead gives a real-terms figure that is far smaller and considerably more useful for planning.