Loan Calculator

What Is a Loan?

Strip away the labels — auto, personal, mortgage, equipment note — and every fixed-rate loan is the same arrangement. A lender advances a sum, and you return it in equal installments over an agreed period, paying rent on whatever is still outstanding. The label decides the paperwork and the collateral. It does not change the arithmetic.

The Numbers That Define a Loan

Five inputs pin a fixed-rate loan down completely. Move any one of them and the installment moves with it; fix all five and there is exactly one payment amount that clears the debt on schedule.

• Loan amount — the price of the thing, or the sum advanced. This is the figure before your own cash goes in.
• Down payment — cash you contribute up front. It comes off the loan amount before anything else happens, so it never has interest charged against it.
• Annual interest rate — the yearly cost of borrowing, entered as a percentage. Enter 7.5, not 0.075.
• Loan term — how long you have to clear the balance, in years. Fractions are allowed, so a 42-month loan is 3.5.
• Repayment frequency — how many installments fall due each year: monthly is 12, quarterly 4, semi-annually 2, annually 1.

From those five the formula derives the only two quantities it actually uses: the periodic rate, which is the annual rate divided by payments per year, and the number of payments, which is the term multiplied by payments per year. A 6% loan paid monthly has a periodic rate of 0.5%, and over 30 years it has 360 payments.

Amortizing, Interest-Only, and Balloon Debt

A fully amortizing loan is one where the scheduled installments, all of them made on time, leave nothing behind. That is the only structure modeled here. Three common alternatives behave differently enough that this number would mislead you.

• Interest-only — the installment covers interest and nothing more, so the balance never falls. That payment is just the amount financed times the periodic rate: on $180,000 at 6% paid monthly it is $900.00 a month, for as long as the arrangement runs.
• Balloon — installments are set as though the term were longer than it is, leaving one large payment at the end. The CFPB describes it as "a large, one-time payment at the end of the loan term", preceded by lower payments in the years before it falls due.
• Revolving credit — a credit card has no fixed term and no fixed installment. The minimum is recalculated from the balance every month, so no amortization formula applies to it at all.

Revolving balances need a model that works forward from a minimum payment rather than backward from a term, which is what you get from the Credit Card Payoff Calculator.

Amount Financed: Why the Down Payment Comes Off First

Interest is charged on what you actually borrow, not on the sticker price, so the down payment is subtracted before the formula runs. On a $32,000 vehicle with $6,000 down, the amount financed is $26,000, and at 6.5% over five years the calculator returns 508.72 a month.

Leave the down payment field blank and it reads as zero, so the installment is calculated on the whole loan amount. Enter a down payment larger than the loan amount and the result comes back negative, which is the calculator's way of saying the two figures are the wrong way round. One thing it does not do is add sales tax, registration, or dealer fees to the price — if those are being financed, fold them into the loan amount yourself.

How Do You Calculate a Loan Payment?

The payment comes from the standard amortization formula, the same one lenders use. The CFPB puts it plainly: lenders work out your principal and interest payment "using a standard mathematical formula and the terms and requirements for your loan". There is no proprietary variation hiding inside a bank's system, and a quoted payment that does not match the formula is a quoted payment with something else folded into it.

The Loan Payment Formula

Payment = F × [ i × (1 + i)^n ] ÷ [ (1 + i)^n − 1 ]

F = loan amount − down payment            (the amount financed)
i = annual rate ÷ 100 ÷ payments per year  (the periodic rate)
n = years × payments per year             (the number of payments)

• F is the amount financed, not the purchase price.
• i is a decimal, not a percentage: 7.5% paid monthly gives i = 0.075 ÷ 12 = 0.00625.
• n counts payments, not years: five years of monthly payments is n = 60.

The bracketed fraction is the annuity factor, and it answers a single question — what share of the balance has to be handed over each period so that interest is covered and the balance still lands on zero after n periods. Multiply that factor by the amount financed and you have the installment.

One convention matters. The annual rate is divided by the number of payments per year with no compounding adjustment, so 9% paid quarterly means 2.25% per quarter. That is how US lenders quote and calculate, and it is also why the payment scales in a straight line with the amount financed: $10,000 at 7% over five years is 198.01 a month, $25,000 on identical terms is 495.03, and $37,500 is 742.54.

Step by Step

By hand it takes about a minute on any calculator with a power key.

• Subtract the down payment from the loan amount. That is F.
• Divide the annual rate by 100, then by payments per year. That is i.
• Multiply the term in years by payments per year. That is n.
• Raise (1 + i) to the power of n, keeping every decimal.
• Multiply that result by i, then divide by the same result minus 1. This is the annuity factor.
• Multiply the annuity factor by F. The answer is your installment.

Step four is where hand calculations go wrong. For a five-year loan at 7.5%, (1.00625) raised to the 60th power is 1.4532944. Round it to 1.45 and a $25,000 loan comes out at $503.47 a month instead of $500.95 — $2.52 too high every month, about $151 across the whole loan, from two dropped decimal places.

Worked Example: $25,000 Over Five Years at 7.5%

A used-car loan with nothing down, repaid monthly.

F = 25,000 − 0 = 25,000
i = 7.5 ÷ 100 ÷ 12 = 0.00625
n = 5 × 12 = 60

Payment = 25,000 × [ 0.00625 × 1.4532944 ] ÷ [ 1.4532944 − 1 ]

Monthly installment

$500.95

Sixty payments of 500.95 come to $30,057.00, so borrowing the money costs $5,057.00 — 16.8% of everything you hand over. The first installment splits $156.25 to interest and $344.70 to principal. By the last month the same $500.95 is $3.11 of interest and $497.84 of principal.

Worked Example: $200,000 With $20,000 Down at 6% for 30 Years

The same formula over a long term, which is where the numbers stop being intuitive.

F = 200,000 − 20,000 = 180,000
i = 6 ÷ 100 ÷ 12 = 0.005
n = 30 × 12 = 360

Payment = 180,000 × [ 0.005 × 6.0225752 ] ÷ [ 6.0225752 − 1 ]

Monthly installment

$1,079.19

Three hundred and sixty payments of 1,079.19 total $388,508.40 against $180,000 borrowed. That is $208,508.40 of interest — more than the loan itself, and 53.7% of every dollar paid. The first payment puts $900.00 toward interest and only $179.19 toward the balance, and principal does not overtake interest inside a single installment until payment 223, in the nineteenth year.

Two Entries That Produce a Believable Wrong Answer

Neither of these triggers an error. Both return a number that looks entirely reasonable, which is what makes them worth checking before you trust a result.

• The rate written as a decimal. Entering 0.07 rather than 7 on a $10,000 three-year loan returns 278.08 a month instead of the correct 308.77. The field wants a percentage.
• The term written in months. A 48-month loan is 4, not 48. Where the term genuinely is not a whole number of years, use a decimal — 42 months is 3.5, which on $20,000 at 6% gives 529.12 a month across 42 payments.

Loan Payment Chart: Cost per $10,000 Borrowed

Because the payment scales in a straight line with the amount financed, one chart covers every loan size. Find your rate and term, then multiply by however many ten-thousands you are borrowing. Every figure below is this calculator's own output for $10,000 with no down payment, repaid monthly.

Divide your amount financed by 10,000 and multiply. Borrowing $25,000 at 7% over five years: 2.5 × 198.01 rounds to 495.03, and the calculator returns 495.03. At $37,500 it is 3.75 × 198.01, or 742.54, which again matches to the cent. The chart doubles as a check on a quote — if a lender's monthly figure sits well above the row for your rate and term, something is being financed that you have not counted.

The Same Chart, Read as Interest

A payment figure hides the cost. These are the totals on that same $10,000 over five years of monthly payments.

Stretching that same $10,000 from three years to five is the standard move for making a payment fit, and the numbers price it. At 5% the interest goes from $789.56 to $1,322.60; at 12% it goes from $1,957.04 to $3,346.40. At every rate in between, the five-year version costs roughly 1.7 times as much as the three-year version. The ratio barely shifts, which means the penalty for a longer term is close to fixed no matter how good your rate is.

How Repayment Frequency Changes the Total

Most loan calculators assume monthly payments. This one asks, because a great deal of real borrowing does not run on a monthly cycle — equipment finance, seller-financed property, and business notes are commonly quarterly or semi-annual. The choice does two things at once: it splits the annual rate into smaller pieces and it changes how many pieces there are.

Here is a $60,000 loan at 9% over five years with nothing down, under each of the four options.

Paying once a year costs $2,397.75 more than paying monthly on an otherwise identical loan, about 16% more interest for the same money over the same five years.

Why Fewer Payments Cost More

The instinct is that fewer compounding periods ought to be cheaper, and in one narrow sense that is right. Dividing 9% by the number of payments produces an effective annual rate of 9.3807% monthly, 9.3083% quarterly, 9.2025% semi-annually, and exactly 9.0000% annually. The least frequent schedule carries the lowest effective rate of the four.

It still costs the most, because the effective rate is not what you pay interest on. You pay interest on the outstanding balance, and a balance reduced once a year sits at close to full size for eleven months longer than one reduced every month. Slower principal reduction beats the small effective-rate advantage every time, which is worth knowing before agreeing to a schedule that suits a lender's administration rather than your wallet.

Getting the Schedule Right

Usually there is no choice to make — the lender's schedule is written into the contract, and the task is entering it correctly rather than defaulting to monthly. Treating a quarterly note as monthly understates things badly: $120,000 at 8% over seven years is $5,638.76 a quarter, and the monthly figure for the same loan, $1,870.35, is not one third of it.

Across the full term that quarterly note costs $37,885.28 in interest, against $37,109.40 if the identical loan were paid monthly. The extra $775.88 is the price of writing four checks a year instead of twelve.

What Moves the Payment: Term, Rate, and Down Payment

Three levers, and they do not pull in the same direction. Two of them lower the installment while raising the total cost. Only one lowers both.

Term: The Lever That Cuts Both Ways

Lengthening the term is the quickest way to make a payment affordable and the most expensive way to do it. On $30,000 at 8% paid monthly:

Going from two years to seven cuts the payment by 66%, from $1,356.82 to $467.59, and multiplies the interest by 3.6, from $2,563.68 to $9,277.56. The relief also tapers sharply: the first extra year takes $416.73 off the monthly payment, the seventh takes $58.41. Past a certain point you are buying almost no breathing room and paying a great deal for it.

Rate: One Point Is Not a Rounding Error

On a $300,000 purchase with $60,000 down — $240,000 financed over 30 years, monthly:

Moving from 5% to 6% adds $150.55 a month and $54,198.00 across the term. From 6% to 7% it is $157.81 a month and $56,811.60. Each additional point costs slightly more than the one before it, because it is charged against a balance that is now falling more slowly. On a long loan even an eighth of a point is real money, and the rate is the part of a deal most open to negotiation.

Down Payment: The Only Lever That Lowers Both

Cash down reduces the amount financed, and everything downstream falls with it. On a $30,000 purchase at 7% over five years, monthly:

The relationship is a straight line, give or take rounding to the cent: each $1,000 down takes about $19.80 off the monthly payment and about $188 off the total interest at these terms. That $188 is what the $1,000 earns you over five years, and it is the figure to weigh against whatever the cash would do if you kept it. A down payment is not automatically the best home for spare money — but unlike the other two levers, it never costs more in the long run.

How to Read Your Result

The calculator returns one number: the installment due each period, principal and interest combined, on the amount financed. It appears without a currency symbol, so it is denominated in whatever currency you entered the loan amount in. Everything else worth knowing is one multiplication away.

Total Repaid and Total Interest

Multiply the installment by the number of payments to get the total repaid, then subtract the amount financed to get the interest.

Total repaid   = installment × years × payments per year
Total interest = total repaid − amount financed

On the $25,000 car loan at 7.5% over five years: 500.95 × 60 = $30,057.00 repaid, of which $5,057.00 is interest. On the $180,000 financed at 6% over 30 years: 1,079.19 × 360 = $388,508.40 repaid, of which $208,508.40 is interest.

The contrast between those two is the whole lesson. Interest is 16.8% of everything paid on the car and 53.7% on the house — not because the mortgage rate is higher, since it is actually lower, but because the term is six times longer. Term, far more than rate, decides whether interest is a footnote or the largest line item in the deal.

Where the First Payment Actually Goes

The installment is constant; what it is made of is not. Interest for a period is the balance at the start of that period multiplied by the periodic rate, and whatever is left of the payment reduces the balance. The CFPB describes the pattern as "a greater percentage is applied to the interest early in the life of the loan while a greater percentage is applied to the principal toward the end."

You can check the first payment yourself. On $180,000 at 6% paid monthly, interest is 180,000 × 0.005 = $900.00, which leaves $179.19 of the $1,079.19 installment to reduce the balance, or 16.6% of it. On the five-year car loan the balance is small relative to the payment, so the split starts the other way round: $156.25 interest against $344.70 principal in the very first month.

This is why the halfway point in time is nowhere near the halfway point in payoff. After 180 of the 360 mortgage payments, with $194,254.20 handed over, the balance is still $127,888.19 and $142,142.39 of what was paid went to interest. Selling or refinancing in year 15 means settling a debt that has barely moved.

Is the Payment Affordable?

The calculator will happily return a payment you cannot make. Lenders test that with the debt-to-income ratio, which the CFPB defines as "all your monthly debt payments divided by your gross monthly income" — their worked example is $2,000 of debt against $6,000 of income, giving 33%. Limits vary by lender and loan product, and there is no single universal cutoff.

A long-standing underwriting convention keeps housing costs near 28% of gross monthly income and total debt near 36%. On a $5,000 gross monthly income that allows $1,400 for housing. Run it backwards through this calculator and $1,400 a month at 6% over 30 years supports about $233,508 financed — enter 233,508 with no down payment and it returns 1,400.00. That is the ceiling before property tax and insurance, which is exactly why the house you can genuinely carry is smaller than that number suggests.

To fold taxes, insurance, and existing debts into the same test, use the Home Affordability Calculator.

Limits: When This Calculator Does Not Apply

The formula is exact for what it models: a fixed-rate, fully amortizing loan with equal payments at regular intervals. Real credit agreements depart from that in specific and predictable ways, and each departure moves the real payment away from the figure here.

0% Financing Returns an Error

Enter 0 for the rate and the page shows an input error rather than a payment. That is the mathematics, not a fault: the denominator is (1 + i) to the power of n, minus 1, and when i is zero that expression equals zero. Division by zero has no answer.

A genuine 0% offer needs no formula anyway — divide the amount financed by the number of payments. $24,000 over 60 months is exactly $400.00 a month; $26,000 over 48 months is $541.67. What is worth reading in the paperwork is whether the promotional rate covers the whole term or only part of it, because the calculator has no way of knowing that a rate changes partway through.

APR Is Not Always the Rate the Payment Is Built From

The input is labeled APR, and on a loan with no fees the APR and the interest rate are the same number. Once there are fees they part company. The CFPB: the APR "reflects the interest rate, any points, mortgage broker fees, and other charges that you pay to get the loan", which is why "your APR is usually higher than your interest rate".

Your lender bills you from the note rate, not the APR. Enter the APR and the payment comes out slightly above what you will actually be charged — helpful for comparing the total cost of two offers, wrong as a budgeting figure. For the payment you will really see, enter the interest rate.

Origination fees deducted from the advance, rather than built into the rate, are handled explicitly by the Personal Loan Calculator.

Structures This Formula Cannot Represent

In each of these cases the number here is not slightly off. It is answering a different question.

• Variable and adjustable rates. The payment holds only for as long as the rate does. When an adjustable-rate mortgage resets, the CFPB notes the payment "will typically be re-calculated based on the new interest rate and the remaining loan term".
• Balloon and interest-only loans, where the installments are deliberately set not to clear the balance by the end of the term.
• Biweekly and accelerated schedules. There is no biweekly option here, and 26 half-payments a year is not the same thing as 12 monthly ones.
• Escrowed costs. Property tax, homeowners insurance, mortgage insurance, and HOA dues are collected alongside a mortgage payment but are not part of principal and interest — the CFPB warns that "the total monthly payment you send to your mortgage company is often higher than the principal and interest payment".
• Precomputed interest. Some small-dollar and older auto contracts fix the total interest at signing, so paying early saves less than it would on an amortizing loan.
• Extra payments. Nothing here models overpaying, and before relying on it, read the contract — the CFPB defines a prepayment penalty as "a fee that some lenders charge if you pay off all or part of your mortgage early".

To watch a balance fall payment by payment, and to see what an overpayment does to the finish date, use the Loan Repayment Calculator.

Rounding, and Your Final Payment

The result is rounded to the cent and lenders round the same way, so the installment you are billed should match. The last one will not. On the $25,000 car loan the unrounded installment is 500.9487, displayed as 500.95; those fractions of a cent accumulate across 60 payments, and the true final payment comes to $500.86 rather than $500.95.

Nine cents is nothing. On longer and larger loans the same effect is bigger, which is why a payoff quote from a lender never exactly equals installment × number of payments. Treat any total-repaid figure calculated that way as accurate to within about one payment, not to the cent.

Which Loan Is This For?

The formula is universal. The costs around it are not. Here is what this calculator covers cleanly for each common kind of borrowing, and what it leaves to a more specific tool.

Auto Loans

It handles the core of a car deal well, because dealers structure financing in exactly this shape: price, minus cash down, over a fixed term, paid monthly. On $32,000 with $6,000 down at 6.5%, four years costs $616.59 a month and $3,596.32 in interest; stretching to six years drops the payment to $437.06 but pushes the interest to $5,468.32. That is $179.53 a month saved for $1,872.00 more paid — the trade every finance office offers, with a price on it.

A trade-in allowance, and sales tax and registration financed into the balance, are handled by the Auto Loan Calculator.

Mortgages

Principal and interest come out right; escrow does not exist here. On a mortgage the number that matters most is the term. On $180,000 financed at 6%, a 30-year schedule costs $208,508.40 in interest and a 15-year schedule costs $93,409.20 — $115,099.20 less, in exchange for $439.75 more a month. Whether that trade is open to you is a debt-to-income question rather than a preference.

Property taxes, homeowners insurance, and HOA dues belong in the monthly figure too, and they are added by the Mortgage Calculator.

Personal and Student Loans

Unsecured borrowing is where the rate range is widest, and it is worth seeing the spread before signing anything. On $15,000 over three years, paid monthly:

The payment hardly moves across that whole range — $687.06 at 36% is only about half as much again as $456.33 at 6% — while the interest is almost seven times higher. That is the trap in short-term unsecured credit: an affordable-looking installment tells you close to nothing about whether the rate is reasonable. Compare the interest column, never the payment column.

Federal student loans carry their own repayment plans, grace periods, and deferment rules, which are modeled in the Student Loan Calculator.

Business Notes and Seller Financing

This is where the frequency selector earns its keep. Equipment finance, seller-financed property, and inter-company notes frequently settle quarterly or semi-annually, and most consumer calculators cannot represent them at all. Enter the schedule as the note is written — term in years, frequency as agreed — and the installment is exact for a fully amortizing agreement.

What it cannot do is an interest-only period followed by a balloon, which is the other common shape in seller financing. For that, work out the interest-only payment separately as amount financed × periodic rate, and treat the balloon as the balance still outstanding when the interest-only period ends.