TVM Calculator — Solve Any of the 5 Time Value of Money Variables
Who this is for: For finance students and exam candidates (MBA core courses, CFA prep, corporate finance homework) who want the five-variable TVM math without a financial calculator at hand — and for anyone double-checking what their BA II Plus just told them.
Not the right tool for: Annuity-due (BGN) problems — this solver is END mode only; shift dates yourself or use your calculator's BGN setting · Amortization schedules — it returns the payment, not the interest-vs-principal split per period
Enter any four of N, I/Y, PV, PMT, and FV — the calculator solves the fifth using the same END-mode TVM math as the BA II Plus.
Quick answer: The TVM equation links five values: PV·(1+i)^n + PMT·[((1+i)^n − 1)/i] + FV = 0. Enter any four of N, I/Y, PV, PMT, FV and the fifth follows — for example, $1,000 saved at the end of each year for 30 years at 8% grows to $113,283.21. Money you pay out is entered as a negative number.
Money out is negative (e.g. -1000)
| Register | Value | Meaning |
|---|---|---|
| N — periods | 30.00 | number of periods |
| I/Y — rate % | 8.0000% | per period, 8 means 8% |
| PV — present | $0.00 | lump sum today |
| PMT — payment | -$1,000.00 | each period, end |
| FV — future | $113,283.21 | lump sum at the end |
| Equation | PV(1+i)^n + PMT·[((1+i)^n−1)/i] + FV = 0 |
|---|---|
| Annuity mode | END (ordinary) — same default as BA II Plus / HP 12C |
| Rate solving | Numerical: grid scan + bisection, −99.9999% to 1000% per period |
| Precision | 4 decimal places |
| Compiled | October 2026 |
What the TVM equation does
Every time-value-of-money problem — a lump sum growing at interest, a savings plan, a loan, even a bond — is the same equation wearing different clothes: PV·(1+i)^n + PMT·[((1+i)^n − 1)/i] + FV = 0, where i is the rate per period. Enter any four of the five variables and the fifth is fixed. This calculator uses the END (ordinary annuity) convention: payments happen at the end of each period, matching the default setting of every exam calculator. Solving for the interest rate has no closed-form solution for general problems, so the site scans a range and bisects — exactly what your handheld calculator does internally, just visible here.
Common uses
- Future value of a savings plan: $1,000 a year for 30 years at 8% → $113,283.21
- How long money takes to double: $10,000 at 7% → 10.24 years
- The annual payment on a $20,000 loan over 5 years at 6% → $4,747.93
- The return a deal really offers: turn $1,000 into $1,500 in 5 years → 8.45% per period
Where these numbers come from
All results are computed in your browser from the standard closed-form formulas (and a numerical root-finder where no closed form exists — rates, IRR, YTM). Formulas follow the ordinary-annuity (END) convention used by the BA II Plus and HP 12C. Educational reference only — not investment, tax, or accounting advice.