Finance Calculator
A universal Time Value of Money (TVM) solver. Pick any variable to solve for — Present Value, Future Value, Payment, Interest Rate, or Number of Periods — and enter the rest.
TVM Calculator — Solve for Any Variable
📊 TVM Results
💡 Summary
📋 Period-by-Period Schedule
| Period | Payment | Interest | Principal | Balance |
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What Is the Time Value of Money?
The Time Value of Money (TVM) is the foundational principle of finance: a dollar today is worth more than a dollar in the future because of its potential earning capacity. This concept underpins virtually all financial decisions.
- Present Value (PV): The current worth of a future sum or stream of payments, discounted at the interest rate. Used for valuing investments, loans, and bonds.
- Future Value (FV): What an investment will grow to over time at a given interest rate. Essential for retirement planning and savings goals.
- Payment (PMT): The periodic payment in an annuity — loan installments, retirement contributions, or lease payments.
- Interest Rate (I/Y): The rate of return per period. For loans, it’s the cost of borrowing; for investments, it’s the expected rate of return.
- Number of Periods (N): Total compounding periods. Monthly loans use months; annual investments use years.
These five variables are interrelated — knowing any four allows you to solve for the fifth. This calculator handles all five cases.
Core TVM Formulas
The general TVM equation that relates all five variables:
For annuity due (beginning-of-period payments), each PMT factor is multiplied by (1+r). The sign convention: negative values represent cash outflows (money you pay), positive values represent cash inflows (money you receive).
Common Use Cases
- Loan Payment: Solve for PMT. Enter PV (loan amount, negative), N (months), Rate, FV = 0.
- Savings Goal: Solve for PMT. Enter FV (target), N (months), Rate, PV = 0 or current balance.
- Investment Growth: Solve for FV. Enter PV (initial, negative), PMT (monthly contributions, negative), N, Rate.
- Mortgage Qualification: Solve for PV. Enter PMT (max affordable), N (360 for 30yr), Rate, FV = 0.
- Rate of Return: Solve for Rate. Enter PV (cost), FV (sale price), N, PMT = 0.
- Time to Pay Off: Solve for N. Enter PV (balance), PMT (payment), Rate, FV = 0.
Finance Calculator FAQ
Why are some values negative?
+TVM calculations use a cash-flow sign convention. Money you pay out (investments, loan amounts, deposits) is negative. Money you receive (future payouts, loan proceeds) is positive. This ensures the formula works correctly — PV and FV should have opposite signs.
What’s the difference between rate per period and annual rate?
+The rate per period is the annual rate divided by the number of compounding periods per year. For a 6% annual rate with monthly compounding: 6% ÷ 12 = 0.5% per period. Always use the per-period rate in TVM calculations.
What is an annuity due vs. ordinary annuity?
+An ordinary annuity makes payments at the end of each period (most loans). An annuity due makes payments at the beginning (rent, some leases). Annuity due payments earn one extra period of interest, making them slightly more valuable.
How do I calculate a mortgage payment?
+Select “Solve for Payment.” Enter PV = −300000 (loan amount), N = 360 (30 years × 12), Rate = 0.583 (7% ÷ 12), FV = 0. The calculator will give you the monthly payment. Use end-of-period timing.
Why can’t the rate be solved in some cases?
+Solving for the interest rate requires an iterative numerical method (Newton-Raphson). In some edge cases — like when cash flows don’t change sign or the equation has no real solution — the solver may not converge. Try adjusting your inputs to ensure a mathematically valid scenario.