The one equation behind almost every finance calculator
Mortgage payments, savings growth, bond pricing, lease payments and retirement projections are all the same underlying relationship, applied to different variables: money now is worth a different amount than the same sum later, at a given interest rate, over a given number of periods. That relationship is called the time value of money, and it links five quantities so tightly that any four of them determine the fifth. This calculator solves for whichever one you are missing.
The five variables
| Variable | Meaning | Typical example |
|---|---|---|
| PV — Present Value | A lump sum today | A deposit, a loan principal, a purchase price |
| FV — Future Value | A lump sum at the end | A savings goal, a loan's payoff amount |
| PMT — Payment | A regular amount each period | A monthly deposit or loan instalment |
| RATE | Interest rate per period | A monthly rate for monthly compounding, not an annual one |
| N — Periods | Number of compounding periods | 360 for a 30-year monthly mortgage |
FV = −PV(1+r)ⁿ − PMT × [(1+r)ⁿ − 1] / rEvery other variable is solved by rearranging this one equation. The calculator does that algebra for you — you only need to know which value you are solving for and supply the other four.
Why the signs matter
Financial calculators follow a cash-flow convention: money you pay out is negative, money you receive is positive. It looks unfamiliar at first but it is what keeps the single equation valid for both saving and borrowing. Depositing into a savings account is a present value you hand over — you enter it as a negative PV, and the future value comes back positive. A loan works the other way: the loan amount you receive is a positive PV, and the payments you make are negative PMT. Getting the signs backwards produces an answer with the wrong sign or a wildly wrong magnitude, which is the most common source of confusion with this kind of calculator.
Matching the rate to the period
The rate and the number of periods must use the same unit of time. A 6% annual rate compounded monthly is 0.5% per period (6 ÷ 12), not 6% per period — entering the annual figure directly overstates the result enormously, since it compounds twelve times too fast. For a 30-year loan paid monthly, N is 360, not 30. This mismatch is the second most common mistake, and it is worth double checking before trusting any result.
Worked example: solving for future value
Depositing $500 a month for 20 years at 7% annual interest, compounded monthly, starting from zero:
- PV = 0 (nothing saved yet)
- PMT = −500 (money paid out each month)
- RATE = 7 ÷ 12 = 0.583% per period
- N = 20 × 12 = 240
- Solve for FV → about
$260,000
Total contributions over 20 years are only $120,000 — the rest, roughly $140,000, is compounding. That gap is the entire case for starting early rather than starting large.
What this calculator is not
It assumes a fixed rate and equal payments at regular intervals — the textbook annuity case. Real mortgages with escrow, variable-rate loans, and irregular contribution schedules need the specialised calculators built for them: Mortgage Calculator and Loan Calculator for borrowing, Investment Calculator for irregular contributions, and Compound Interest Calculator for a simpler lump-sum-plus-rate view without solving for an unknown. This tool is for the general case underneath all of them, and for anyone who already knows four of the five numbers and needs the fifth.