The formula
How it works
A general time-value-of-money solver. Pick which of the five variables you want to find — future value, present value, payment, number of periods or interest rate — and enter the other four. Money paid out is negative; money received is positive.
FAQ
Why are some values negative?
The five variables are tied by one equation that only balances if inflows and outflows have opposite signs. Enter money leaving your pocket (a deposit or loan payment) as negative and money coming in (a withdrawal or loan received) as positive. The calculator then returns the missing value with the correct sign.
What counts as one period?
A period is whatever the rate matches. For a loan paid monthly, a period is a month and the rate is the monthly rate — the annual rate divided by 12. For an annual investment, a period is a year. Keep N and the rate on the same footing and the answer is consistent.
What is the difference between present value and future value?
Present value is what a sum of money is worth today, while future value is what it grows into after earning interest over time. The two are linked by the interest rate and the number of periods, which is exactly what this calculator solves for.
Why does the calculator say there is no solution?
No solution usually means the inputs describe an impossible cash-flow pattern, such as a payment or rate combination that never balances the equation. Double-check the signs on PV, PMT and FV, and confirm the rate and number of periods make sense together.
Why is the interest rate solved differently from the other variables?
Present value, future value, payment and periods all have a direct algebraic formula, but the rate appears in a way that cannot be isolated algebraically. The calculator instead searches numerically for the rate that makes the equation balance, narrowing in on the answer step by step.
How do I convert an annual rate to a periodic rate?
Divide the annual rate by the number of periods per year — for example, a 6% annual rate becomes 0.5% per month. Enter that periodic rate along with a matching number of monthly periods so N and the rate stay consistent.
Does this calculator handle a lump sum with no regular payments?
Yes — just set the payment (PMT) to 0 and enter only a present value or future value. The calculator still solves for any of the other variables using the same time-value-of-money equation.
About the finance calculator
This is a general time-value-of-money (TVM) calculator, the engine behind loans, savings, annuities and investment maths. Five quantities — the number of periods, the interest rate, the present value, the payment and the future value — are linked by a single equation, and knowing any four lets you solve for the fifth. It is the same tool built into financial calculators, generalised so one page handles many money questions.
How to use it
Choose the variable you want to solve for, then fill in the other four. Follow the sign convention: money you pay out is negative, money you receive is positive. For example, depositing $1,000 now (PV = −1,000) and $100 a month (PMT = −100) for 120 months at 0.4167% a month gives a future value of about $17,175 — the balance you could withdraw.
The formula
All five variables satisfy , where payments fall at the end of each period. The calculator rearranges this equation to isolate whichever variable you are solving for. The interest rate has no closed-form solution, so it is found numerically by searching for the rate that makes the equation balance.
Where it is used
Anyone comparing loans, planning savings, valuing an annuity or checking an investment return uses time-value-of-money maths, often without naming it. This calculator exposes it directly, so you can answer questions the single-purpose tools do not — such as what rate turns a set of payments into a target balance, or how many periods a plan takes. It is the Swiss-army knife of personal finance calculations.