Finance
Finance Calculator (TVM)
Solve for any unknown in the time value of money equation.
$
$
Future Value (FV)
$12,693,857/ period
Based on standard time-value-of-money calculations.
Periods120
Rate (I/Y)6%
PV-$10,000
PMT-$100
Finance
Solve for any unknown in the time value of money equation.
Future Value (FV)
$12,693,857/ period
Based on standard time-value-of-money calculations.
A TVM solver is a financial calculator that applies the fundamental equation of finance to find any missing variable in the relationship between money now, money later, and periodic cash flows. It uses standard formulas from corporate finance and banking to compute future value (what your money grows to), present value (what future money is worth today), payment (the periodic amount you save or borrow), or time (how long your money compounds or a loan runs). Any interest rate environment—savings accounts, loans, investments—uses the same underlying logic.
The calculator solves the core TVM equation: PV(1+i)^n + PMT × [((1+i)^n - 1) / i] + FV = 0. You input four of the five variables (N = periods, I/Y = annual interest rate, PV = present value, PMT = periodic payment, FV = future value), then select which one to solve for. The calculator uses algebraic manipulation or numerical methods to compute the unknown, instantly showing the result. Negative signs denote cash outflows; positive, inflows.
FV = -PV(1+i)^n - PMT × [((1+i)^n - 1) / i]PV grows exponentially at rate i per period over n periods, and periodic payments PMT accumulate with compound interest. The result is the total future value. Similar formulas rearrange to solve for PV, PMT, or N. Interest rate i is the annual rate divided by 100 and represents the per-period rate (annual ÷ 12 for monthly periods).
| Input | Result | Notes |
|---|---|---|
| Periods: 120 | Rate: 6% | PV: -10,000 | PMT: -100 | Solve: FV | FV: 23,456 | 10-year investment: £10,000 initial + £100/month at 6% annual growth compounds to £23,456. |
| Periods: 360 | Rate: 4.5% | PV: -300,000 | FV: 0 | Solve: PMT | PMT: -1,520 | 30-year mortgage: £300,000 borrowed at 4.5% requires £1,520/month payment to reach zero balance. |
| Periods: unknown | Rate: 8% | PV: -50,000 | PMT: -500 | Solve: N | N: 143 periods | £50,000 saved at £500/month with 8% annual return takes 143 months (11.9 years) to reach target. |
PV (present value) is the amount you have or owe today; FV (future value) is what that money becomes in the future after interest accrues or debt grows. If you deposit £1,000 today and it earns 10%, the PV is £1,000 and the FV is £1,100 after one year.
In finance, negative represents cash leaving your wallet (a payment or investment), and positive represents cash entering. Your lender receives your £500/month payment (negative from your view), and the loan balance decreases. This sign convention ensures the math works consistently across all five variables.
No—the calculator assumes a fixed interest rate throughout the entire period. If your loan rate changes halfway through, calculate each portion separately (e.g., first 5 years at 3%, next 5 at 5%), then combine the results manually.
The calculator works in nominal (unadjusted) dollars. To find the real return, subtract inflation from your interest rate (e.g., 5% nominal minus 2% inflation = 3% real return), then use that adjusted rate in the calculator.
The calculator handles zero-rate scenarios correctly: money doesn't grow, so FV equals PV plus the sum of all payments. For example, £10,000 + (£100 × 120 months) = £22,000 with no interest.
Not directly in this calculator—it solves for FV, PV, PMT, and N only. To find interest rate, try different rates manually and watch the FV change until it matches your target. Many financial tools offer a dedicated rate-solver function.