Future value

Future value is the amount a sum invested today will grow to after n periods of compounding at rate r: FV = PV × (1 + r)^n. It is the mirror image of present value.

ByHoang TruongUpdated June 30, 2026

FrameworkTime value of money

See it move

Loading infographic...

You deposit €5,000 today in an account paying 4% a year. Compounding means each year's gain itself earns a return the following year, so after four years the balance reaches €5,000 × 1.04⁴ ≈ €5,850, €850 of growth, more than the €200-a-year simple interest would have produced, because the later gains are earning on earlier gains too.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

FV = PV \times (1+r)^n

Variables

$F V$: Future value (€)
$P V$: Present value (amount invested today) (€)
$r$: Interest rate per period (decimal)
$n$: Number of compounding periods (periods)

Projects a present sum forward at compound interest.

Check yourself

PracticeCORE

You deposit €4,000 today in an account paying 6% per annum, compounded annually. What is the future value of this deposit after three years, to the nearest euro?

Select an answer to check your understanding.