How it works
A time-value-of-money problem has five moving parts: the amount you start with (present value), the amount you end with (future value), the periodic payment, the interest rate per period, and the number of periods. The distinctive strength of this Finance Calculator (TVM) is that it solves for any one of those five variables once you supply the other four — making it a single tool that replaces a shelf of single-purpose calculators.
Set the unknown variable to zero (or leave it blank) and fill in the rest. The engine then inverts the algebra — or, for the rate variable, iterates numerically — to recover the missing figure. This is the same five-variable solver architecture used in financial calculators and spreadsheet TVM functions.
The calculator works in monthly periods. You enter an annual interest rate and a term in years; internally it divides the rate by 12 and multiplies the years by 12. Payments are assumed to occur at the end of each month (an ordinary annuity). Cash you pay out is entered as a negative; cash you receive is positive.
The formula
FV = PV·(1 + r)^n + PMT·[((1 + r)^n − 1) / r]
Where:
| Symbol | Meaning |
|---|---|
| FV | Future value (end balance) |
| PV | Present value (starting lump sum) |
| PMT | Fixed monthly payment |
| r | Periodic (monthly) interest rate |
| n | Total number of periods (months) |
To solve for a different unknown, rearrange algebraically; for the rate, no closed-form inverse exists so the calculator uses numerical iteration until both sides balance.
Worked example
Suppose you want to know the future value of a plan with these inputs:
- Present value: $10,000
- Monthly payment: $250
- Annual rate: 6%
- Years: 20
Step 1 — convert to monthly figures.
- Monthly rate r = 0.06 / 12 = 0.005
- Number of months n = 20 × 12 = 240
Step 2 — compound the present value.
FV_PV = 10,000 × (1.005)^240
(1.005)^240 ≈ 3.31020, so FV_PV ≈ 10,000 × 3.31020 = $33,102
Step 3 — compound the monthly payment stream.
FV_PMT = 250 × [(1.005^240 − 1) / 0.005]
(1.005^240 − 1) / 0.005 ≈ 462.0409, so FV_PMT ≈ 250 × 462.0409 = $115,510
Step 4 — add the two components.
FV = 33,102 + 115,510 = $148,612
So after 20 years you would have roughly $148,612.
Now the universal-solver twist: if instead you knew you needed $148,612 and had $10,000 to start at 6% over 20 years, you could leave FV fixed and solve for PMT — the calculator would return about $250/month. Swap any four values and recover the fifth. That five-way flexibility is what sets this tool apart from calculators that only compute future value.
Things to watch
- End-of-period assumption. This solver treats payments as occurring at month-end. If your payments are at the start of each month, results will differ slightly.
- Rate sign convention. Enter the annual rate as a plain percentage (e.g., 6 for 6%). Entering 0.06 would be treated as 0.006%.
- Payment direction. For consistency, treat contributions as outflows (negative) and the returned balance as an inflow (positive). Mixing signs can cause the solver to return a nonsensical value.
- Estimate, not professional advice. TVM results assume a constant rate and level payments over the entire term. Real-world products may include fees, taxes, rate changes, or irregular contributions that materially change outcomes.