Loan Payment Calculator
From the principal, APR, term and payment frequency the calculator derives the periodic rate r = APR/m, the number of payments N = m·t, the level payment PMT = P·r / (1 − (1 + r)⁻ᴺ), the total paid and the total interest, with a preview of the first amortization rows.
The payment, and what it hides
An amortising loan is repaid by a series of identical payments, and the size of that payment is not obvious from the principal and the rate. Each payment covers the interest accrued since the last one and puts whatever is left towards the balance — so the split shifts every period even though the total never does.
This calculator finds the level payment that clears the balance exactly at the end of the term, then reports the total paid, the total interest, and the first few rows of the amortisation schedule.
The payment alone is the number most people want, and it is the least informative one. Two loans with similar payments can differ enormously in what they cost, because the term does as much work as the rate.
The total interest line is the corrective. It is the difference between everything paid and the amount borrowed, and on a long loan it is frequently comparable to the principal itself — which is far more visible as a figure than as a rate.
How to use this calculator
- Enter the principal The amount borrowed. The calculator is currency-agnostic and performs no conversion, so the unit you enter is the unit reported back.
- Enter the annual percentage rate As a percentage, so 5 rather than 0.05. It is a nominal annual rate: the periodic rate is derived from it by dividing.
- Enter the term in years Always years, whatever the payment frequency. The number of payments is computed from the term and the frequency together.
- Set the payments per year Twelve for monthly, 26 for fortnightly, 4 for quarterly. It divides the rate and multiplies the number of payments at the same time.
The formula, and where it comes from
r = APR / 100 / m N = m·t PMT = P·r / (1 − (1 + r)⁻ᴺ) interest = N·PMT − P
The periodic rate is the annual rate shared out across the payments in a year. That is a nominal convention rather than a compounding calculation — twelve monthly periods at a twelfth of the annual rate slightly exceed the annual rate once compounded, which is why the effective cost is a little above the quoted one.
The payment formula comes from requiring the present value of all the payments to equal the amount borrowed. The denominator is what a stream of N payments of one unit is worth today at that rate; dividing the principal by it scales the stream so it exactly repays the loan.
That denominator approaches 1 as the term lengthens, so the payment approaches the interest on the principal alone and stops falling meaningfully. Extending a loan past a certain point buys almost nothing in payment relief while adding years of interest.
Total interest is derived rather than accumulated: everything paid, minus the amount borrowed. It therefore reconciles exactly with the payment by construction. A zero rate is handled separately, since the formula would divide by zero — there the payment is simply the principal split evenly.
What each input means
- P Principal — form field “Loan principal”
- The amount borrowed at the outset, in any currency, unconverted.
- APR Annual rate — form field “Annual percentage rate (%)”
- The nominal annual percentage rate. Divided by 100 and then by the payment frequency to give the rate charged each period. Units: percent per year.
- t Term — form field “Term (years)”
- Length of the loan in years. Fractional terms are accepted. Units: years.
- m Payments per year — form field “Payments per year”
- How often a payment is made. It appears twice — dividing the rate and multiplying the count — so raising it does not simply raise the cost. Units: payments per year.
Worked examples
Every number below is produced by the same calculation engine the tool above runs. Nothing here is typed by hand, so the walkthrough cannot drift from what you get when you enter the same values yourself.
A thirty-year mortgage
200,000 at 5% over 30 years, paid monthly. A long term at a moderate rate, which is where total interest grows most dramatically.
Inputs Loan principal = 200000, Annual percentage rate (%) = 5, Term (years) = 30, Payments per year = 12
- Principal P = 200000.00
- APR 5%
- Term 30 years, 12 payments per year (360 total)
- Periodic rate r = 5% / 12 = 0.416667% per period
- Formula PMT = P · r / (1 − (1 + r)⁻ᴺ)
- Payment PMT = 1073.64 per period
- Total paid 386511.57 = 360 · 1073.64
- Total interest 186511.57
- Payment 1 interest 833.33, principal 240.31, balance 199759.69
- Payment 2 interest 832.33, principal 241.31, balance 199518.38
- Payment 3 interest 831.33, principal 242.32, balance 199276.06
- Payment 4 interest 830.32, principal 243.33, balance 199032.74
Result Payment = 1073.64 per period; total interest 186511.57
Total interest over the term is close to the amount borrowed. That is the characteristic result for a thirty-year loan at this kind of rate, and it is invisible in the monthly payment, which looks modest.
In the first amortisation row, interest takes the large majority of the payment and only a small remainder reduces the balance. That ratio inverts slowly across the term, and it is why early overpayments are worth so much more than late ones.
A five-year car loan
25,000 at 6% over 5 years, paid monthly. A short term at a higher rate — the opposite balance of the mortgage.
Inputs Loan principal = 25000, Annual percentage rate (%) = 6, Term (years) = 5, Payments per year = 12
- Principal P = 25000.00
- APR 6%
- Term 5 years, 12 payments per year (60 total)
- Periodic rate r = 6% / 12 = 0.5% per period
- Formula PMT = P · r / (1 − (1 + r)⁻ᴺ)
- Payment PMT = 483.32 per period
- Total paid 28999.20 = 60 · 483.32
- Total interest 3999.20
- Payment 1 interest 125.00, principal 358.32, balance 24641.68
- Payment 2 interest 123.21, principal 360.11, balance 24281.57
- Payment 3 interest 121.41, principal 361.91, balance 23919.66
- Payment 4 interest 119.60, principal 363.72, balance 23555.93
Result Payment = 483.32 per period; total interest 3999.20
Despite the higher rate, total interest is a small fraction of the principal. Term dominates rate in determining total cost, which is the comparison the two examples are here to make.
The first payment already puts most of its value against the balance, because sixty payments do not leave much room for interest to accumulate. The schedule is far less lopsided than the mortgage's.
Reading the result
Why early payments are mostly interest
Interest each period is charged on the balance still outstanding. That balance is at its largest at the start, so the interest portion is too, and only the remainder of the level payment reduces it — which is why progress feels slow for the first years of a long loan.
What the payment excludes
It is principal and interest only. Insurance, property taxes, arrangement fees and any early-repayment charge are outside the model, so a real instalment is typically larger than the figure shown.
Nominal against effective
Dividing the annual rate by the frequency is a convention, not a compounding step. Twelve months at a twelfth of the rate compound to slightly more than the annual rate, so the effective cost sits a little above the quoted APR.
When you would use this
Comparing terms at the same rate
Running the same principal and rate over different terms shows the trade directly: a shorter term raises the payment and cuts the total interest, often by far more than the payment rises.
Working backwards from affordability
Adjusting the principal until the payment matches what can be afforded gives the amount that can sensibly be borrowed, with the total interest visible alongside it.
Assumptions and limitations
What this calculator assumes
- The rate is fixed for the whole term and every payment is made on time and in full.
- Payments are level, and the schedule clears the balance exactly at the end of the term.
- The rate entered is nominal and annual, divided by the payment frequency to give the periodic rate.
- No fees, insurance, taxes, overpayments or early settlement are modelled.
Where it stops being the right tool
- Fixed-rate loans only: a variable or tracker rate, or an introductory period, cannot be represented.
- Only the first few amortisation rows are shown rather than the full schedule.
- Interest-only periods, balloon payments and deferred starts are out of scope.
- No tax treatment, and no distinction between how different jurisdictions accrue daily interest.
Common mistakes
Converting the term to match the payment frequency
Why it happens. Having entered 12 payments a year, giving the term in months feels consistent. The number of payments is already the product of the term and the frequency, so doing it yourself multiplies twelvefold.
How to avoid it. Leave the term in years always. If the payment comes back implausibly small, this is almost certainly why.
Entering the rate as a decimal
Why it happens. The formula uses r as a decimal, so 0.05 looks like the right thing to type. This field expects a percentage, and 0.05 is read as one-twentieth of a percent.
How to avoid it. Enter 5 for five percent. The periodic-rate line shows what the calculation actually used, which confirms the field in one glance.
Comparing loans on the payment alone
Why it happens. It is the number quoted in advertising and the one that affects a monthly budget, so it stands in for the cost of the loan.
How to avoid it. Compare total interest instead. A longer term lowers the payment while raising what the loan costs, and only the total shows that.
Frequently asked questions
What does APR mean here?
The nominal annual percentage rate. It is divided by 100 and then by the number of payments per year to give the rate charged in each period, which is the rate the payment formula actually uses.
Why does the early payment go mostly to interest?
Because interest is charged each period on the balance still outstanding, and that balance is largest at the start. The payment is level, so the interest portion falls and the principal portion rises as the balance comes down.
Can I model fortnightly payments?
Yes — set the payments per year to 26 and leave the term in years. More frequent payments reduce the balance sooner, so the total interest is a little lower than under a monthly schedule at the same rate.
Does the payment include anything besides the loan?
No. It covers principal and interest only. Insurance, taxes, arrangement fees and early-repayment charges are all outside the calculation, so a real instalment is usually higher.