Time Value of Money Calculator
The five time-value variables, solving for whichever one you do not know — present value, future value, payment, rate or number of periods.
Five quantities are linked by one equation: present value, future value, payment, rate and number of periods.
How the time value of money calculator works
Five quantities are linked by one equation: present value, future value, payment, rate and number of periods. Know four and the fifth follows.
Rate and periods have no closed form when payments are involved, so they are found numerically. Everything else is direct algebra on FV = PV(1+r)ⁿ + PMT[((1+r)ⁿ−1)/r].
Formula: FV = PV(1+r)ⁿ + PMT[((1+r)ⁿ − 1)/r]
Worked examples
| Inputs | Result | Note |
|---|---|---|
| Future value of 10k plus 500/month | 100,133.6407 | about 100,000 |
| What rate reaches 50k? | 5.7267 | solves numerically |
| How long to reach 50k? | 7.5519 | about 8 years |
FAQFrequently asked questions
What is the time value of money?
The principle that a dollar today is worth more than a dollar later, because it can earn a return in the meantime.
Which variable can I solve for?
Any of the five — present value, future value, payment, rate or periods — given the other four.
Why are rate and periods solved numerically?
Because with regular payments the equation has no closed-form solution for either. Every calculator does the same thing.
Does compounding frequency matter?
Yes, though less than people expect. Monthly rather than annual compounding at 6% adds about 0.17 percentage points of effective return.
Is this the same as a savings calculator?
It is the general form. A savings, loan or annuity calculator is this equation with some variables fixed.
Where these figures come from
- CFA Institute — Quantitative Methods: The Time Value of Money — the discounting, annuity and IRR conventions used here
- US Federal Reserve — Regulation Z (Truth in Lending), APR calculation — why APR includes fees where a nominal rate does not
- ASIC MoneySmart — the Australian regulator's own consumer calculators
Last checked: September 2026. These are the standard textbook formulas; the conventions named are those of the CFA Institute curriculum and ISO 80000 usage.