Annuities and savings Updated November 2026

Annuity formula (future value)

An ordinary annuity is a series of equal payments at the end of each period. Its future value is FV = PMT x ((1 + r)^n - 1) / r, where r is the rate per period and n the number of payments. This is the formula for what a regular savings plan grows to.

Syntax

FV = PMT x ((1 + r)^n - 1) / r

Part	What it is
`PMT`	Payment per period, the same every period
`r`	Interest rate per period
`n`	Number of payments

Examples

PMT = 100 per year, r = 5%, n = 3
FV = 100 x (1.05^3 - 1) / 0.05

Result: FV = 315.25

Excel: =FV(5%, 3, -100)

PMT = 200 per month, 6% a year, 10 years
FV = 200 x ((1 + 0.005)^120 - 1) / 0.005

Result: FV = 32,775.87

Excel: =FV(6%/12, 120, -200)

PMT = 1,000 per year, r = 8%, n = 10
FV = 1,000 x (1.08^10 - 1) / 0.08

Result: FV = 14,486.56

Common mistakes

Using the annual rate with monthly payments; divide the rate by 12 and count n in months.
Applying the ordinary annuity formula to payments made at the start of each period; those are an annuity due and are worth (1 + r) times more.
Checking the result against PMT x n: the future value must be larger than the plain sum of the deposits when r is positive (315.25 versus 300 above).

Practice Annuity formula (future value)

These drills check your answer on live data, free, no account needed.

Future value of a savings planYou deposit $50 at the end of every month into an account earning 3.25% APR, compounded monthly. How much will you have after 35 years?
Monthly saving to reach a goalYou want $15,000 in 30 years. Your account earns 3.25% APR, compounded monthly. How much must you deposit at the end of each month?

Questions

What is the difference between an ordinary annuity and an annuity due?

In an ordinary annuity payments come at the end of each period; in an annuity due they come at the start. Each payment in an annuity due earns one extra period of interest, so FV_due = FV_ordinary x (1 + r).

How do I calculate the future value of an annuity in Excel?

=FV(rate, nper, pmt, [pv], [type]) with the payment entered as a negative number. =FV(5%, 3, -100) returns 315.25; add type 1 for payments at the start of the period.

Present value of an annuityHow to find the present value of equal payments with PV = PMT x (1 - (1 + r)^-n) / r. Worked examples, Excel PV and why this is the loan formula in disguise.
Annuity dueAn annuity due has payments at the start of each period, so it is worth the ordinary annuity value times (1 + r). PV and FV examples, Excel type = 1, errors.
Monthly deposit for a savings goalThe monthly deposit needed to reach a target is PMT = FV x r / ((1 + r)^n - 1). Examples for 10,000 in 5 years and 50,000 in 10 years, Excel PMT and errors.
Future valueHow to calculate the future value of a lump sum with FV = PV x (1 + r)^n, step-by-step examples, the Excel FV function with its sign convention, and errors.