TVM Calculator
Fill in four of the five time-value-of-money numbers and solve the fifth, with the formula shown.
Free, no sign-upRuns in your browserHow we calculate
- Periods per year
- 12
- Timing
- End of period
How this was calculated
- Core identity: PV × (1+i)^n + PMT × (1 + i×b) × ((1+i)^n − 1) / i + FV = 0, with i the rate per period, n the number of periods and b = 1 for start-of-period payments.
- Money you pay in counts as negative and money you receive as positive; this tool shows deposits as positive amounts for readability.
- Rate and period count are solved numerically or with logarithms; the other values have closed forms.
Educational estimate with a fixed rate and level payments, not financial advice.
What a TVM calculator does
A TVM (time value of money) calculator rests on one idea: a dollar today is worth more than a dollar later, because today's dollar can earn interest. The TVM calculator links five numbers: present value (PV), future value (FV), the regular payment (PMT), the interest rate per period and the number of periods (N). Enter four and it solves the fifth, exactly like the TVM keys on a financial calculator or the PV, FV, PMT, NPER and RATE functions in Excel.
The formula
With i the rate per period and n the number of periods, the five values satisfy PV × (1+i)n + PMT × ((1+i)n − 1) / i + FV = 0. Payments at the start of each period (an annuity due) are multiplied by an extra (1+i). Cash you pay out is negative and cash you receive is positive; this page shows your deposits as positive numbers to keep it readable.
Worked examples
Future value: saving $200 a month for 10 years at 6% compounded monthly (i = 0.5%, n = 120) grows to $200 × ((1.005)120 − 1) / 0.005 = $32,775.87, of which $24,000 is your money.
Payment: to reach $50,000 in 10 years at 5% compounded monthly from nothing you need to save about $321.99 a month. Periods: starting with $10,000 and adding $200 a month at 5%, you hit $50,000 after about 126 months, roughly 10.5 years.
Common mistakes
- Mixing frequencies: if you pay monthly, use 12 periods per year, not 1.
- Entering the annual rate as the periodic rate. This tool divides the annual rate by the periods per year for you.
- Ignoring timing. Paying at the start of each period raises the future value by a factor of (1+i).
- Expecting an answer for an impossible goal, such as a target below what you already have with a zero rate.
Results assume a constant rate and equal payments. Real returns vary, and taxes and fees reduce them.
Frequently asked questions
What does a TVM calculator do?
It links present value, future value, payment, interest rate and number of periods. Enter four of them and it solves the fifth.
What is the time value of money formula?
PV × (1+i)^n + PMT × ((1+i)^n − 1) / i + FV = 0, where i is the rate per period and n the number of periods. Payments at the start of a period are multiplied by an extra (1+i).
How much do I need to save each month to reach $50,000?
At 5% compounded monthly for 10 years starting from zero, about $321.99 a month. The result changes with the rate and the timeline.
What is the difference between ordinary annuity and annuity due?
An ordinary annuity pays at the end of each period; an annuity due pays at the start, so each payment earns one extra period of interest.
Why does the calculator say there is no solution?
The goal may be unreachable, for example a future value below your starting amount with only positive deposits, or periods per year of zero.