Finance Calculator uses the rates, dates, fees, and assumptions entered or explicitly cited by this formula. It does not replace a current quote, eligibility decision, filing calculation, contract, or professional financial advice.
This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.
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Five-key TVM solver
Choose one value to calculate
Select the missing key, then enter only the other four values. Rates and period counts always use the same period basis.
Step 1
What do you want to calculate?
FVFind the ending value after the entered periods and recurring payments.
Results
Your calculated value
Future Value (FV)$110.00
Based on 1 year at 10% per year, with payments at the end of each period.
PMT × N
$0.00
Growth factor
1.1×
Equation check
Balances to 0
Currency changes formatting only. The underlying equation uses signed currency units and keeps full precision until display.
Educational time-value arithmetic only; this is not a rate quote, approval, appraisal, or investment forecast.
Cash-flow comparison
PV, PMT, and FV magnitudes
Bar lengths use absolute magnitudes; labels preserve the entered or solved signs.
PV
-$100.00
PMT
$0.00
FV
$110.00
Complete result
Five-key value table
The calculated key is highlighted; every rate and count uses the same selected period.
Key
Meaning
Value
N
Number of periods
1 year
I/Y
Rate per year
10%
PV
Present value
-$100.00
PMT
Periodic payment
$0.00
FVCalculated
Future value
$110.00
Finance calculator guide
Understand present value, future value, payments, rate, and time
A five-key finance calculator solves one missing time-value-of-money variable from the other four. The useful part is not only the answer: keeping the periods, payment timing, and cash-flow signs visible makes the scenario understandable and checkable.
PV
Present valueThe signed cash flow at time zero: what is received or invested today.
FV
Future valueThe signed ending cash flow after the final period.
PMT
Periodic paymentAn equal signed cash flow made at the beginning or end of every period.
I/Y
Interest rateThe percentage rate for one period. It is annual only when one period is one year.
N
Number of periodsThe count of payment and interest periods on the same time basis as I/Y.
01
The central idea
The time value of money
Would you rather receive $500 today or the same $500 one year from now? Money available today can be saved, invested, or used to avoid a borrowing cost. That opportunity is why equal dollar amounts at different dates do not necessarily have equal economic value.
The five-key equation puts a present amount, a future amount, equal periodic payments, an interest rate, and a number of periods on one timeline. With end-of-period payments, its common form is:
TVM equation0 = PV(1 + i)N + PMT(1 + i)N − 1i+ FV
Here i is I/Y written as a decimal. Beginning-of-period payments receive one additional factor of (1 + i).
02
Worked example
How $100 becomes $121 at 10%
Suppose $100 is invested for two yearly periods at 10% per year with no recurring payment. From the investor's viewpoint, the $100 paid today is an outflow, so enter PV = −$100 and PMT = $0, then solve for FV.
Year 1$100 × 1.10 = $110
The first year earns $10, so the balance becomes $110.
Year 2 interest$110 × 0.10 = $11
The second year earns $10 on principal plus $1 on prior interest.
Future value$110 + $11 = $121
The calculator returns FV = +$121, opposite in sign to the initial outflow.
03
Input discipline
Use one viewpoint and opposite cash-flow signs
Money paid out
Investments, deposits, and loan payments are normally negative from the payer's viewpoint. For example, a $250 monthly deposit can be entered as PMT = −$250.
Money received
Loan proceeds, withdrawals, and the ending amount received are normally positive from the same viewpoint. Switching viewpoints is valid only when every related sign switches consistently.
If PV, PMT, and FV all point in the same direction, a rate or period solution may not exist. That is not a formatting issue; it means the entered cash flows do not balance under the selected model.
04
Timing and units
Make I/Y, N, and PMT describe the same period
Monthly example
For five years of monthly payments, N is 60. I/Y must be a monthly rate under the convention you intend; entering an annual rate as a monthly rate would overstate growth dramatically.
End-of-period payment
An ordinary annuity pays after interest is applied for each period. This is the common default for loan and savings examples.
Beginning-of-period payment
An annuity due pays before that period's interest is applied, so each payment affects the balance for one additional period.
The calculator deliberately does not guess payments per year or compounds per year. Convert a quoted nominal or effective annual rate according to the product's actual convention before treating it as a periodic I/Y input.
05
Practical interpretation
What each solve mode can answer
FV: What ending amount follows from today's value and a recurring cash flow?
PV: What value today is equivalent to a declared future amount and payment stream?
PMT: What equal periodic cash flow balances the beginning and ending values?
I/Y: What constant nonnegative periodic rate balances the entered cash flows?
N: How many matching periods are required under a constant rate and payment?
These are conditional mathematical answers, not forecasts or offers. Real loans and investments may add fees, taxes, irregular dates, changing rates, missed payments, day-count rules, or market risk that a level-payment equation does not model.