Finance Calculator
The time-value-of-money solver: give any four of present value, future value, payment, term and rate, and it solves for the fifth — with sign conventions explained.
Finance Calculator: with the default inputs, solved value is 50,969.84.
The one value left over is computed from the other four.
Cash today. Negative if it leaves your pocket, positive if you receive it.
The level cash flow each period, with the same sign rule.
Cash at the end — a balloon, a balance, or 0 for a loan paid off in full.
Count of periods, not years: 10 years of monthly payments is 120.
Nominal annual rate. It is divided by the periods per year below.
Payments and compounding share this frequency.
Dollars for PV/PMT/FV, periods for N, percent per year for the rate.
- In words
- Future value: $50,969.84
- Present value
- -$10,000.00
- Payment per period
- -$200.00
- Future value
- $50,969.84
- Periods
- 120
- Nominal annual rate
- 6%
- Effective annual rate
- 6.1678%What the nominal rate is worth once it compounds every period.
- Sum of all payments
- -$24,000
- Total interest
- $16,970Everything that came in minus everything that went out.
Assumptions
- One constant periodic rate, with compounding at the payment frequency.
- Level payments; the nominal annual rate is divided by the periods per year.
- Cash out is negative and cash in is positive; a consistent set of five values sums to zero.
- Fees, taxes and inflation are not included.
| Period | Cash in (+) / out (−) | Interest | Balance |
|---|---|---|---|
| 1 | $200.00 | $50.00 | $10,250.00 |
| 2 | $200.00 | $51.25 | $10,501.25 |
| 3 | $200.00 | $52.51 | $10,753.76 |
| 4 | $200.00 | $53.77 | $11,007.53 |
| 5 | $200.00 | $55.04 | $11,262.56 |
| 6 | $200.00 | $56.31 | $11,518.88 |
| 7 | $200.00 | $57.59 | $11,776.47 |
| 8 | $200.00 | $58.88 | $12,035.35 |
| 9 | $200.00 | $60.18 | $12,295.53 |
| 10 | $200.00 | $61.48 | $12,557.01 |
| 11 | $200.00 | $62.79 | $12,819.79 |
| 12 | $200.00 | $64.10 | $13,083.89 |
Balance is positive when the money is yours and negative when you owe it.
How this is worked out
The formula
PV(1 + i)^n + PMT(1 + i·type) × [ ((1 + i)^n − 1) ÷ i ] + FV = 0 i = nominal annual rate ÷ periods per year n = number of periods type = 1 when payments arrive at the beginning of the period, 0 at the end Sign convention: cash you pay out is negative, cash you receive is positive. The rate is found by bisection — no closed form exists once PMT ≠ 0.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- The one value left over is computed from the other four.Future value (FV) · Present value (PV) · Payment (PMT) · Number of periods (N) · Interest rate (I/Y)
- Present value (PV)
- Cash today. Negative if it leaves your pocket, positive if you receive it.in dollars · defaults to -10000
- Payment (PMT)
- The level cash flow each period, with the same sign rule.in dollars · defaults to -200
- Future value (FV)
- Cash at the end — a balloon, a balance, or 0 for a loan paid off in full.in dollars · defaults to 50969.84
- Number of periods (N)
- Count of periods, not years: 10 years of monthly payments is 120.from 0 to 1200 · whole numbers only · defaults to 120
- Interest rate (I/Y)
- Nominal annual rate. It is divided by the periods per year below.a percentage · from -50 to 200 · defaults to 6
- Periods per year
- Payments and compounding share this frequency.Monthly (12) · Quarterly (4) · Semi-annually (2) · Annually (1)
- Payments occur(under More options)
- Rent and leases are usually due at the beginning; loans and savings deposits at the end.End of period (ordinary annuity) · Beginning of period (annuity due)
What you get back
- Solved valuemain answer
- Dollars for PV/PMT/FV, periods for N, percent per year for the rate.
- In words
- Present value
- Payment per period
- Future value
- Periods
- Nominal annual rate
- Effective annual rate
- What the nominal rate is worth once it compounds every period.
- Sum of all payments
- Total interest
- Everything that came in minus everything that went out.
What this assumes
- One constant periodic rate, with compounding at the payment frequency.
- Level payments; the nominal annual rate is divided by the periods per year.
- Cash out is negative and cash in is positive; a consistent set of five values sums to zero.
- Fees, taxes and inflation are not included.
About this calculator
Every loan, lease, savings plan and bond price is the same equation wearing different clothes. Five quantities — present value, payment, future value, number of periods and interest rate — are tied together by one identity, and knowing any four fixes the fifth. This is the calculator that solves it in either direction, the way the TVM keys on an HP 12C or a BA II Plus do.
The five values it opens with are a consistent set — $10,000 down, $200 a month for 120 months at 6% grows to $50,969.84 — so you can switch Solve for to any of the five and watch it reproduce the value already in the box. Change any four of them and the fifth follows.
Signs are the whole trick
The equation only balances if you say which way the money moves. Cash leaving your pocket is negative; cash arriving is positive. So:
- Saving: you deposit $10,000 today (PV = −10,000) and $200 a month (PMT = −200), and in 10 years you take out a positive FV.
- Borrowing: the bank hands you $20,000 (PV = +20,000), you repay a negative PMT, and FV = 0 when the loan is gone.
- A bond: you pay the price today (PV = negative), collect positive coupons (PMT), and receive the positive face value at maturity (FV).
If every number carries the same sign, no interest rate on earth balances them, and the calculator says so instead of inventing an answer.
How to use it
Pick what you want to solve for, fill in the other four, and set the periods per year. N is a count of periods, not years — ten years of monthly payments is 120. The rate you enter is the nominal annual rate; it's divided by the periods per year, which is exactly what a lender means by "6% compounded monthly". Switch payments to the beginning of the period for leases, rent and most annuities-due; leave them at the end for loans and ordinary savings.
Reading the results
The solved value is the headline. Beneath it, all five quantities are shown together so you can check the whole picture at once, plus the effective annual rate — 6% compounded monthly is really 6.168% a year — and the sum of the payments. The total interest line is simply everything that came in minus everything that went out; it is negative when you were the one paying.
Where it can mislead
The model assumes one constant rate, level payments, and compounding that matches the payment frequency. Real loans have fees (use APR instead of the note rate to compare them), real investments have variable returns, and a rate solved from a single lump-sum-to-lump-sum pair says nothing about the path in between. Solving for N usually gives a fraction of a period; lenders round up, so the last payment is smaller than the rest.
Frequently asked questions
▸Why is my payment negative?
Because the calculator uses the standard cash-flow sign convention. If the bank gives you money (PV positive), the payments must flow the other way, so PMT comes out negative. The size is what matters; the sign only records the direction.
▸What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period; an annuity due pays at the beginning, so every payment earns one extra period of interest. Switching to beginning-of-period multiplies the annuity factor by (1 + i) — usually a few percent.
▸Why does solving for the rate need a numerical method?
Once there is a payment stream, the equation is a polynomial in (1 + i) of degree n and cannot be rearranged for i. This calculator brackets the answer and bisects until the equation balances to within a rounding error, which is what financial calculators do internally.
▸Is the rate I enter the same as APR?
Only when there are no fees. APR under Regulation Z folds prepaid finance charges into the rate, so a loan with an origination fee has an APR above its note rate. Use the note rate here to get the payment, and APR to compare offers.
▸How do I model a balloon payment?
Put the balloon in FV as a negative number (you pay it) when you are the borrower, then solve for PMT. The payments amortize only the part of the balance that isn't left in the balloon.
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