Online TVM Solver: N, I/Y, PV, PMT, FV Time Value of Money
A five-key time-value-of-money solver for loans, savings, annuities, leases and investments. Enter any four of N, I/Y, PV, PMT and FV — plus payments per year and ordinary or annuity-due timing — and solve for the fifth, following the standard cash-flow sign convention. Rates are solved numerically and all calculations run locally in your browser.
Time Value of Money (TVM) Solver
Given the other variables, solve for any one of N, I/Y, PV, PMT or FV.
Sign convention: cash outflows are negative, inflows are positive (as on a financial calculator). E.g. an initial deposit is negative and the future payout is positive.
Time-Value-of-Money Solver Guide
Solve for N, I/Y, PV, PMT or FV
The TVM solver solves the standard time-value-of-money equation for any one unknown given the other four values. It models loans, savings, annuities and leases: present value (PV), periodic payment (PMT), future value (FV), number of periods (N) and periodic interest rate (I/Y). Enter what you know, choose which variable to solve for, and press Compute.
01 Sign convention and inputs
Cash-flow sign convention applies: money you pay out is negative, money you receive is positive. For a typical loan you receive PV (positive) and make PMT payments (negative); for a savings plan you make negative deposits and receive a positive FV. P/Y (payments per year) sets how many periods a year contains — 12 for monthly loans, 1 for annual — and I/Y is always the nominal annual rate. End/Begin controls whether payments occur at the end (ordinary annuity) or start (annuity due) of each period.
To solve, pick the target variable in the “Solve for” row; that field becomes disabled because it will be calculated. Fill in the other four and press Compute. To solve a different variable, select it in “Solve for” and the previously solved field becomes editable again.
- N — total number of periods (years × P/Y for monthly loans)
- I/Y — nominal annual interest rate in percent
- PV — present value (loan amount or starting balance)
- PMT — periodic payment
- FV — future value (remaining balance or target amount)
- P/Y — payments per year; also sets compounding periods per year
Solver controls
- Solve for: NCalculate the number of periods needed.
- Solve for: I/YCalculate the annual interest rate.
- Solve for: PVCalculate the present value.
- Solve for: PMTCalculate the periodic payment.
- Solve for: FVCalculate the future value.
- N / I/Y / PV / PMT / FVInput fields for the five TVM variables. The solve target is disabled.
- P/YPayments (and compounding periods) per year.
- End / BeginPayments at period end (ordinary annuity) or start (annuity due).
- ComputeSolves for the selected variable and displays the result.
- Remember the sign convention: inflows positive, outflows negative — it resolves most “wrong sign” confusion.
- For a mortgage, set P/Y = 12 and N = years × 12.
- If a loan is fully paid off, FV = 0; set it explicitly.
- Use Begin for leases and rent, which are typically paid in advance.
A free online time-value-of-money (TVM) calculator. Solve for any one of N (number of periods), I/Y (annual interest rate), PV (present value), PMT (periodic payment) or FV (future value) given the other four, with end-of-period or beginning-of-period (annuity-due) payments and a payments-per-year setting. Computed locally in your browser.
Solving for a variable
Use the top switch to choose which variable to solve for (N, I/Y, PV, PMT or FV), enter the other four known values and press Calculate. The rate is an annual percentage divided by P/Y into a periodic rate, and N is counted in periods. Beginning-of-period payments multiply PMT by (1+i) for an annuity due.
Sign convention
Follow the TI BA II Plus convention: outflows are negative and inflows positive. For example, money you deposit today is PV=-1000, while payments you receive each period are PMT=100. Getting signs wrong will flip or break the result.
Use cases and disclaimer
Useful for loans, mortgages, savings goals, annuities and leases, as well as CPA/CFA study. Rates are solved by bisection with a Newton fallback. Results depend on your inputs and standard formulas; they are not investment, tax or accounting advice — verify real decisions against the actual contract and consult a professional.
FAQ
QWhat is the TVM sign convention?
Outflows are negative and inflows positive. Depositing 1000 today means PV=-1000; receiving 100 each period means PMT=100. Wrong signs flip the result.
QWhat does P/Y mean?
Payments (and compounding periods) per year. For monthly loans enter 12; the annual rate is divided by 12 and N is measured in periods.
QWhat is the difference between end and begin?
End means ordinary-annuity payments at period end; Begin means annuity-due payments at period start, multiplying PMT by (1+i).
QWhy does solving I/Y take a moment?
The interest rate cannot be expressed in closed form for TVM, so it is found numerically by bisection with a Newton fallback, which takes a few iterations.