Time Value of Money Calculator (TVM Solver)
5-variable time value of money solver. Enter any four of PV, FV, PMT, N, and rate — solve for the fifth. Beginning/end-of-period toggle.
Time Value of Money Calculator
The universal 5-variable time-value-of-money solver. Enter any four of present value, future value, payment, number of periods, and the periodic rate — leave the one you want to find, and the solver computes it. Use the sign convention outflows negative, inflows positive (e.g. a deposit is negative, a payout positive).
How to Use the TVM Solver
Pick what to solve for
Choose PV, FV, PMT, N, or rate from the "Solve for" dropdown. That field is disabled — you fill in the other four.
Mind the sign convention
Cash you pay out is negative; cash you receive is positive. A $10,000 deposit today is PV = −10000. This is the same convention Excel and financial calculators use.
Match the rate to the period
If N counts months, the rate is the monthly rate (annual ÷ 12). If N counts years, use the annual rate. The solver doesn't assume a compounding frequency — you set it via the period.
Set payment timing
Ordinary annuities pay at the end of each period (most loans, savings deposits). Annuity-due pays at the beginning (leases, some rents). The toggle shifts every payment one period.
The Time Value of Money, Explained
One Equation, Five Unknowns
Every time-value-of-money problem is the same underlying equation rearranged. A present value grows by compounding; a stream of equal payments (an annuity) accumulates or discounts; and the two combine into a single identity: PV·(1+i)ⁿ + PMT·(1+i·type)·[((1+i)ⁿ − 1)/i] + FV = 0. Give the solver any four of the five variables and it isolates the fifth. For PV, FV, PMT and N this is straightforward algebra; for the rate there's no closed form, so the tool finds it numerically by bisection (the same way a financial calculator's IRR/rate key works).
Why the Sign Convention Matters
The equation only balances if inflows and outflows carry opposite signs. If you deposit $10,000 today (an outflow from you, PV = −10,000) and contribute −$200/month, the future value comes back positive — the money you'll receive. Mixing signs incorrectly is the single most common TVM error and produces nonsense results. When in doubt: money leaving your pocket is negative.
"The rate is the only TVM variable with no algebraic solution. Calculators and spreadsheets all iterate to find it — this tool brackets the root and bisects to a rate that makes the cash flows balance to the penny."
Ordinary Annuity vs Annuity-Due
Timing changes the answer. An ordinary annuity pays at period-end (a typical mortgage or savings plan); an annuity-due pays at the start (most leases, insurance premiums, rent). Because annuity-due payments sit one period earlier, they earn one extra period of growth — multiplying the annuity term by (1 + i). For a 30-year stream at a meaningful rate, that shift is not trivial.
Where You'll Use It
TVM underlies loan payments, bond pricing, retirement projections, lease-vs-buy analysis, NPV, and every DCF valuation. It's the first thing taught in corporate finance and the most-tested concept on the CFA Level I exam. Master the five-variable solver and most "finance math" becomes plugging four knowns into one equation.
10 Facts About the Time Value of Money
A dollar today is worth more than a dollar tomorrow — because today's dollar can be invested to earn a return.
The rate is the only TVM variable with no closed-form solution; it must be found by iteration.
Annuity-due payments are worth (1 + i)× more than ordinary-annuity payments, all else equal.
At 7% annual growth, money doubles in about 10 years — the Rule of 72 (72 ÷ rate%).
TVM is the foundation of net present value (NPV) and discounted cash flow (DCF) valuation.
Excel's PV, FV, PMT, NPER and RATE functions all solve this same identity.
The sign convention (outflows negative) is shared by every financial calculator and spreadsheet.
Bond prices are simply the present value of coupons (an annuity) plus the PV of face value.
The rate must match the period: a monthly N needs a monthly rate (annual ÷ 12).
TVM is the single most-tested topic on the CFA Level I quantitative methods section.
Frequently Asked Questions
- Money flowing out of your pocket is negative; money coming in is positive. A deposit or loan principal you pay down is negative; a payout or maturity value you receive is positive. The TVM equation only balances when inflows and outflows carry opposite signs — the same convention Excel and HP/TI financial calculators use.
- The rate appears inside (1 + i)ⁿ and in the annuity term simultaneously, producing a high-degree polynomial with no general closed-form root. So every tool — this one, Excel's RATE, and financial calculators — finds it numerically. This solver brackets the root and bisects until the cash flows balance to within a penny.
- It must match the period. If N counts months, use the monthly rate (annual ÷ 12). If N counts years, use the annual rate. The solver is period-agnostic — it never assumes a compounding frequency, so you control it through the period and rate you enter.
- Use annuity-due (payments at the beginning of the period) for leases, insurance premiums, and most rent — anything paid up front. Use ordinary (end of period) for most loans and savings deposits. Annuity-due payments earn one extra period of growth, so they're worth (1 + i)× more.
- Yes. Set PV to the loan amount (positive, money you receive), FV to 0, N to the number of payments, the rate to the monthly rate, and solve for PMT — the result is negative (your outflow). For a full month-by-month breakdown, use our dedicated Loan Amortization Schedule Generator instead.
- Usually a sign-convention problem: if every cash flow has the same sign, no rate or period can make them balance (you can't earn a return on money that only ever flows one way). Make sure at least one value has the opposite sign of the others. It can also mean the scenario genuinely has no real solution.
- Yes — it implements the identical TVM identity and sign convention used by Excel (PV/FV/PMT/NPER/RATE) and HP 12C / TI BA II Plus calculators. Given the same inputs and payment timing, results match to rounding.
- A shortcut: divide 72 by the annual return rate to estimate how many years money takes to double. At 8%, about 9 years; at 6%, about 12. It's an approximation of the exact TVM answer (solve for N with PV negative and FV = 2×|PV|, PMT = 0) and is remarkably accurate for rates between 4% and 12%.
- No. It's a math tool that computes a single missing TVM variable from the four you supply. It makes no assumptions about inflation, taxes, or whether a given return is realistic. Use it for the arithmetic; consult a licensed adviser for decisions.
- Yes, for the core arithmetic: set PV to your current balance (negative), PMT to your monthly contribution (negative), N to months until retirement, the rate to your assumed monthly return, and solve for FV. Remember it uses a single fixed rate and ignores inflation, taxes, and sequence-of-returns risk — for a fuller retirement view, pair it with a dedicated retirement or safe-withdrawal calculator.
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