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Time Value of Money Calculator

Move one lump sum between present and future value using periodic nominal or continuous compounding.

Published

Lump-sum value
Future value
$16,470.09
Input value
$10,000.00
Arithmetic value change
$6,470.09
Annual rate
5%
Term
10 yr
Compounding convention
monthly
Growth/discount factor
1.647

Moves one lump sum between two dates; it does not determine whether the entered annual rate is appropriate.

$
%

Nominal annual rate for finite frequencies; continuously compounded annual rate in continuous mode.

yr

Results update as you type.

One lump sum between two dates

Choose future value to move a present amount forward, or present value to move a future amount backward. This calculator handles one lump sum only. It excludes payment streams, cash-flow schedules, taxes, product-specific day counts, and rate-selection advice.

Source-backed formulas

For a nominal annual rate r, n finite compounding periods per year, and term t years:

FV=PV(1+rn)nt\text{FV}=\text{PV}\left(1+\frac{r}{n}\right)^{nt}

Present value is the transparent algebraic rearrangement:

PV=FV(1+rn)nt\text{PV}=\frac{\text{FV}}{\left(1+\frac{r}{n}\right)^{nt}}

For a continuously compounded annual rate:

FV=PVexp⁡(rt),PV=FVexp⁡(rt)\text{FV}=\text{PV}\exp(rt), \qquad \text{PV}=\frac{\text{FV}}{\exp(rt)}

Publisher conventions and example

The finite frequency choices are 1, 2, 4, 12, 52, and 365 periods per year. Weekly 52 and daily 365 are calculator conventions, not universal product day-count standards. Algebraic rearrangement, value-change subtraction, and display rounding are transparent publisher arithmetic.

The default 5% rate, 10-year term, and 10,000 present value are illustrative, not recommended or representative. With monthly compounding:

(1+0.0512)120=1.6470094977\left(1+\frac{0.05}{12}\right)^{120} =1.6470094977

The future value is $16,470.09 after rounding. With continuous compounding, exp(0.5)=1.6487212707, producing $16,487.21. At a zero-year term, every valid mode has a factor of 1.

Limits

The annual rate is nominal for finite frequencies and continuously compounded in continuous mode. Nominal and real bases must be consistent, but this calculator does not choose a basis or an appropriate rate. The result includes no periodic cash flows, forecast, advice, or product-compatibility claim.

Sources

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Time Value of Money Calculator updated at