A time-value-of-money solver. Enter any four of N (periods), rate, present value, payment, and future value — and solve for the fifth. The classic financial-calculator engine, free in your browser.
Time Value of Money solver
The time value of money (TVM) links five variables: the number of periods (N), the interest rate per period, the present value (PV), the periodic payment (PMT), and the future value (FV). Given any four, the fifth is determined. This is the engine inside every financial calculator and spreadsheet — it powers loan payments, savings projections, bond pricing, and retirement planning. This tool uses the standard end-of-period convention.
Sign convention matters: money you pay out is negative and money you receive is positive. For example, investing $10,000 today (PV = −10,000) and adding $200 per period (PMT = −200) for 120 periods at 0.5% per period solves to a future value of about $50,970 (FV positive, because you receive it). Flip the signs and you'll get an error or a sign-flipped answer, so keep outflows negative and inflows positive.
Pick what to solve for, fill in the other four, and the calculator returns the missing value instantly.
Enter cash you pay as negative and cash you receive as positive. This keeps the equation balanced and the result correct.
The rate must match the period. For monthly periods, use the monthly rate (annual ÷ 12). N is the total number of periods.
The five time-value-of-money variables — present value, future value, payment, rate and number of periods — are linked by one relationship. Give any four and the fifth is determined. This is the engine behind every financial calculator: loan payments, savings goals, retirement projections and bond prices are all the same equation solved for a different unknown. The one convention that causes endless confusion is sign: money flowing out is negative and money flowing in is positive, so a loan has a positive PV and negative payments, while a savings plan has negative payments and a positive FV.
PV(1 + r)^n + PMT × [ ((1 + r)^n − 1) ÷ r ] + FV = 0Solve for PMT, PV or FV algebraically; for r or n, iteraten = log(FV ÷ PV) ÷ log(1 + r), when PMT = 0Sign convention: outflows negative, inflows positivewhere:
Assumptions: The commonest error is mismatching r and n: an annual rate with monthly periods. Always divide the annual rate by the number of periods per year and multiply the years by the same figure.
One scenario, four different questions, all from the same equation.
ResultOne equation — FV $35,817, doubling in 11.9 years, or $244.08/month
Recognising that these are the same calculation is what makes financial arithmetic tractable. A mortgage payment, a retirement projection and a bond price differ only in which variable is unknown and which sign convention applies.