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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.

For related single-payment moves and compounding conventions, use the Future Value Calculator and Present Value Calculator, the Continuous Compound Interest Calculator for the continuously compounded case, and the Effective Annual Yield Calculator to annualize a periodic rate.

Sources

Frequently asked questions

What formulas does the time value of money calculator use?
For finite compounding, future value is present value times (1 plus the rate divided by periods per year) raised to the periods-times-years power, and present value is the algebraic rearrangement. For continuous compounding, future value is present value times e raised to the rate-times-years power, with present value as the reciprocal factor.
Which compounding frequencies are available?
The finite 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.
What is outside this calculator's scope?
It moves one lump sum only. It excludes payment streams, cash-flow schedules, taxes, product-specific day counts, and rate-selection advice, and the annual rate is nominal for finite frequencies or continuously compounded in continuous mode.

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Time Value of Money Calculator updated at

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