FinCalcs

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.

Solve for

Money out is negative (e.g. -1000)

solved below ↓
Solved FV
$113,283.21
value at the end of period N
RegisterValueMeaning
N — periods30.00number of periods
I/Y — rate %8.0000%per period, 8 means 8%
PV — present$0.00lump sum today
PMT — payment-$1,000.00each period, end
FV — future$113,283.21lump sum at the end
Sign check: money you pay out is negative, money you receive is positive. A deposit stream (PMT negative) earns a positive FV; a loan you receive (PV positive) pays back negative PMTs. Need the payment instead of a lump sum? The NPV calculator works on whole cash flow streams.
END mode (ordinary annuity) — payments at the end of each period, same default as the BA II Plus and HP 12C. Educational reference, not investment advice.
Core facts
EquationPV(1+i)^n + PMT·[((1+i)^n−1)/i] + FV = 0
Annuity modeEND (ordinary) — same default as BA II Plus / HP 12C
Rate solvingNumerical: grid scan + bisection, −99.9999% to 1000% per period
Precision4 decimal places
CompiledOctober 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.

Frequently Asked Questions

Why does my payment come out negative?
Sign convention: money you pay out is negative, money you receive is positive. If you deposit $1,000 a year (PMT = −1,000), the future value comes back positive — the account pays you at the end. A loan works the mirror way: you receive the principal (PV positive), so the payments are negative.
What is END vs BGN mode?
END (ordinary annuity) assumes payments at the end of each period; BGN (annuity due) assumes the start. This calculator is END mode, which is the default on the BA II Plus and HP 12C. For annuity-due problems, multiply the END result for FV by (1+i) — or set BGN on your handheld.
How do I enter monthly problems?
Keep the units consistent: for a 5-year monthly loan at 6% per year, enter N = 60 and I/Y = 0.5 (6% ÷ 12). The calculator never converts periods for you — neither does the BA II Plus.
Why can't the interest rate be solved with a formula?
For general problems with both PV and PMT nonzero, the TVM equation is an nth-degree polynomial in (1+i), and polynomials of degree 5 and up have no general closed-form solution. Calculators (and this page) find the root numerically — scan for a sign change, then bisect to as many decimals as you need.
Is this the same as the BA II Plus?
The TVM math is identical — same equation, same END-mode default. What this page does not replicate: BGN mode, the amortization (AMORT) worksheet, cash-flow worksheets, statistics, and the bond worksheet. For those, use the handheld.

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