Why is the rate per period and not annual?

TVM math is period-agnostic — you just need rate-per-period and N-total-periods to match. For a 30-year mortgage at 6% annual compounded monthly: rate per period = 6/12 = 0.5%; N = 30 x 12 = 360. For annual compounding at 6% over 30 years: rate per period = 6%; N = 30.

How does it solve for I (interest rate)?

Iteratively via Newton-Raphson — there is no closed-form solution for I given the other 4. The algorithm starts at I = 1% and refines until f(I) is essentially zero. Converges in under 100 iterations for any realistic input.

What sign convention does it use?

Enter all amounts as positive numbers. Internally, PV is treated as a cash OUTFLOW (you invest it) and PMT + FV as INFLOWS (you receive them). For a loan, the math handles the flipped direction automatically.

Can I use this for mortgage payments?

Yes — solve for PMT with PV = loan amount, FV = 0 (loan paid off), N = total monthly periods, I = monthly rate. For a $300,000 30-year mortgage at 6.75% APR: PV=300000, FV=0, N=360, I=0.5625 -> PMT around $1,946 per month.

Why does it sometimes return "No solution"?

The TVM equation does not always have a real solution — e.g., asking "what rate makes $100 grow to $50 in 10 periods with $50 per period contributions" has inconsistent cash flows. The calculator returns "No solution" when the inputs are algebraically irreconcilable.

Why is the rate per period and not annual?

TVM math is period-agnostic — you just need rate-per-period and N-total-periods to match. For a 30-year mortgage at 6% annual compounded monthly: rate per period = 6/12 = 0.5%; N = 30 x 12 = 360. For annual compounding at 6% over 30 years: rate per period = 6%; N = 30.

How does it solve for I (interest rate)?

Iteratively via Newton-Raphson — there is no closed-form solution for I given the other 4. The algorithm starts at I = 1% and refines until f(I) is essentially zero. Converges in under 100 iterations for any realistic input.

What sign convention does it use?

Enter all amounts as positive numbers. Internally, PV is treated as a cash OUTFLOW (you invest it) and PMT + FV as INFLOWS (you receive them). For a loan, the math handles the flipped direction automatically.

Can I use this for mortgage payments?

Yes — solve for PMT with PV = loan amount, FV = 0 (loan paid off), N = total monthly periods, I = monthly rate. For a $300,000 30-year mortgage at 6.75% APR: PV=300000, FV=0, N=360, I=0.5625 -> PMT around $1,946 per month.

Why does it sometimes return "No solution"?

The TVM equation does not always have a real solution — e.g., asking "what rate makes $100 grow to $50 in 10 periods with $50 per period contributions" has inconsistent cash flows. The calculator returns "No solution" when the inputs are algebraically irreconcilable.

Finance Calculator (TVM 5-Key Solver)

Time-value-of-money solver — solve for Present Value, Future Value, Payment, Periods, or Interest rate given the other four. The HP-12C and TI BA-II Plus core in a free browser tool.

Result

Solved: Future Value

$160,677.00

End-of-period (ordinary annuity). Per-period rate, not annual.

PV (Present Value)$10,000.00Healthy
FV (Future Value)$160,677.00Note
PMT (Payment / period)$100.00Healthy
N (Periods)360Healthy
I (% per period)0.5000%Healthy
Total contributed (PV + sum of PMT)$46,000.00
Interest earned / paidPositive: account grew via compound returns.$114,677.00

Source: Standard TVM equation per CFA Institute Quantitative Methods. Solve-for-rate uses Newton-Raphson convergence.

Not financial advice — Assumes constant rate and constant payment over all periods. For variable-rate or variable-payment scenarios, use a dedicated mortgage or cash-flow calculator. Sign convention: enter all amounts positive; PV is treated as an outflow, PMT + FV as inflows.

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How to use this calculator

Pick "Solve for" — the variable you want the calculator to compute.
Enter the other 4 variables. Use rate PER PERIOD (annual rate divided by compounding frequency) and N as total period count.
Read the breakdown. The solved value is highlighted; the inputs that drove the calculation are listed for verification.

About this tool

The Time Value of Money (TVM) is the foundational equation of finance: a dollar today is worth more than a dollar in the future because money can earn interest. This calculator is the standard 5-key TVM solver from the HP-12C and TI BA-II Plus financial calculators — pick which variable to solve for (PV / FV / PMT / N / I) and enter the other four. Use it for mortgage payment math, bond pricing, retirement projection, lease analysis, savings goals, and any scenario reducible to a constant-rate, constant-payment cash flow.

Frequently asked

PV (Present Value) is what something is worth TODAY. FV (Future Value) is what it will be worth AT THE END of N periods. PV grows to FV via compounding; FV discounts back to PV via dividing by (1+r)^N.

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