Personal finance
Annuity future value calculator
Paying a constant instalment for a number of periods, find the capital accumulated at the end.
When to calculate the future value of an annuity
A financial annuity is a sequence of equal payments at regular intervals. Its future value is the capital you end up with at the close of the last period: each instalment is capitalised for the time it has left to run, so the first one earns interest for almost the whole term and the last one for almost none.
It is the calculation behind regular savings plans, defined-contribution pension funds, recurring-premium policies and any programmed savings goal. Compared with a lump-sum investment, an annuity spreads entry risk over time but accrues less interest for the same total capital paid in.
The distinction between ordinary and due annuities is about when the payment falls: an instalment paid at the end of the period makes the annuity ordinary, one paid at the start makes it due. In the second case every instalment has one extra period to grow, and the future value is larger by a factor of (1 + i).
Numeric example: €1,000 paid in at year end for 20 years at 3% a year produces 1,000 × ((1.03)^20 − 1) / 0.03 = €26,870.37. Total paid in is €20,000, so accrued interest is €6,870.37. With payments at the start of each year the figure rises to €27,676.49.
Common mistakes
- Entering an annual rate with monthly instalments: the rate must be restated on the instalment frequency, if necessary with the equivalent compound rate calculator.
- Failing to state whether the annuity is ordinary or due: over long horizons the difference is worth a whole period of interest.
- Confusing the future value with the total paid in: the future value includes both the payments and the interest they produced.
Frequently asked questions
What is the formula for the future value of an annuity?
For an ordinary annuity M = R × ((1 + i)^n − 1) / i, where R is the instalment, i the rate per period and n the number of periods. For an annuity due the result is multiplied by (1 + i).
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity the instalment is paid at the end of each period, in an annuity due at the start. In the latter every payment accrues interest for one extra period, so the future value is higher by a factor of (1 + i).
What happens if the rate is zero?
With a zero rate no interest accrues and the future value equals the total paid in, i.e. instalment × number of periods. The calculator handles this case explicitly.
Does the calculation account for inflation, taxes or fees?
No: the result is gross. For a realistic estimate you should subtract tax on financial returns and the product's fees, and allow for the loss of purchasing power caused by inflation.
How this calculation works
Ordinary annuity: M = R × ((1 + i)^n − 1) / i. Annuity due: M = R × ((1 + i)^n − 1) / i × (1 + i). With i = 0 the future value is simply R × n. The rate i must be a decimal and refer to the same frequency as the instalments.