Present & Future Value Calculator

Ordinary annuity versus annuity due

An ordinary annuity pays at the end of each period; an annuity due pays at the start. Every annuity-due payment therefore earns one extra period of interest, which makes the whole stream worth exactly (1 + rate per period) times more. Rent is an annuity due; loan repayments are ordinary annuities. Mixing them up produces an error of one period's interest — small monthly, meaningful over thirty years.

Nominal rate versus effective annual rate

Seven per cent compounded monthly is not 7 per cent a year — it is 7.229 per cent, because each month's interest earns interest afterwards. The effective annual rate above converts the quoted nominal rate into what you actually earn, which is the only way to compare products with different compounding frequencies.

Why the zero-rate case matters

The standard annuity formulas divide by the rate, so a rate of exactly zero produces a division by zero and a blank or NaN result. Many calculators fail here. At zero per cent the answer is simply the payment multiplied by the number of periods, and this page handles that case explicitly rather than breaking.

Timing within the period is worth more than it looks

An ordinary annuity pays at the end of each period; an annuity due pays at the beginning. The only difference is that every payment in an annuity due earns one extra period of compounding, which makes it worth exactly (1 + i) times the ordinary equivalent. At a 7 per cent annual rate that is a 7 per cent difference in the final figure for the same money, and it is why rent and insurance premiums are structured as annuities due while loan payments and most coupons are not.

The discount rate is the assumption that does most of the work, and it is a choice rather than a fact. For a decision about your own money, the defensible rate is the return genuinely available on the alternative use of that money at similar risk. Inflating the rate to make a project look attractive, or deflating it to justify a purchase, produces a number that is internally consistent and externally meaningless. Running the calculation at two or three rates shows how much the conclusion actually depends on the guess.

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