Time value of money calculator
Future value of a sum, and discounting future money back to today.
Fill in the fields and the result will appear here automatically.
Computes both sides of (1+i)^n: future value multiplies today’s amount by the factor, while present value divides a future amount. A nominal 12% with monthly compounding corresponds to 12.68% effective annual growth, so frequency has its own input. This is a single-amount model without later cash flows. Present value is an estimate at the chosen rate, rather than a recommendation about what to pay for a promised payment.
How it works
Formula and logic
For nominal annual rate r in percent and frequency m (12, 4 or 1 per year), i=r/(100m), n=t×m and F=(1+i)^n. FV=A×F; PV=A/F; effective annual rate = [(1+i)^m−1]×100%. Duration t uses positive years without rounding; r≥0. A fractional n extends the growth curve between periods and does not specify a real contract’s partial-period rule. One amount lies at the start for FV or at the end for PV; there are no deposits or withdrawals.
Example
100,000 at 12% a year compounded monthly becomes 181,669.67 after five years. At 0%, both values equal the original amount. For 10,000 at 12% annually, quarterly compounding and 0.125 years, the result is 10,148.89 over 0.5 periods, rather than one period.
Fields and units
- What to compute — list option
- Amount — $
- Nominal annual rate, % — unitless
- Term, years — years
- Compounding frequency — list option
How to use
- — Choose whether to compute future or present value.
- — Enter the amount, the rate and the term.
- — Choose how often interest is compounded.
- — For discounting, enter the future amount.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Microsoft FV: future value with consistent rate and period count Microsoft PV: present value and consistent rate and duration units
- Limitation
- One amount and a constant nonnegative nominal annual rate. Inflation, fees, taxes, payment risk and contractual partial-period rules are excluded. This is neither full borrowing cost nor a reliability assessment of a promised payment.
FAQ
How should I interpret the present value of a promised payment?
At the entered rate, 500,000 due in eight years with 9% annual compounding is equivalent to 250,933.14 today. This is conditional: the formula does not assess the chance of payment or other costs.
Why is the effective rate higher than the nominal one?
Because interest is added more than once a year and starts earning on itself. A nominal 12% compounded monthly works out at 12.68% a year.
How is this different from a compound interest calculator?
That one models a deposit growing with regular top-ups. Here there is a single sum and two directions in time — forward and back — with no contributions.
Which rate should I discount at?
The return you could realistically get from an alternative investment of similar risk. That is the price of giving up the money today.
Can changing the rate alone make the result real?
First align nominal or real cash flows with a rate on the same basis. Subtracting inflation from a nominal rate is only an approximation. Adjusting an already calculated nominal future balance to purchasing power requires a separate price adjustment.