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Calculate monthly payments and view a full amortization schedule.
How is the monthly payment calculated?
The monthly payment uses the standard amortization formula: M = P × [r(1+r)^n] / [(1+r)^n – 1], where P is the loan principal, r is the monthly interest rate (annual rate / 12), and n is the total number of payments.
What is an amortization schedule?
An amortization schedule shows the breakdown of each payment into principal and interest. Early payments are mostly interest, but over time more goes toward reducing the principal. This schedule helps you see exactly how your loan balance decreases over time.
A Short History of Loans, Interest, and Amortisation
Borrowing money is as old as agriculture. The earliest surviving legal code, Hammurabi's Code (~1754 BCE in Babylon), included statutory interest caps: 20% per year on silver loans and 33⅓% on grain. Roman law subsequently capped rates and the lex Genucia (342 BCE) briefly banned interest entirely, though enforcement was sporadic. The mathematics of compound interest entered Western Europe through Leonardo Fibonacci's «Liber Abaci» (1202), which introduced Hindu-Arabic numerals to the Mediterranean and worked out the compound-interest problems that medieval merchants had been computing awkwardly with Roman numerals. The Florentine and Genoese banking houses (Medici, Peruzzi, Bardi) refined the practice into the modern double-entry ledger. The Swiss mathematician Jacob Bernoulli stumbled across the constant e ≈ 2.71828 in 1683 while studying the limit of compound interest as the compounding frequency approached infinity: the number that governs all continuous-compounding finance emerged out of asking how rich a deposit could become. The closed-form amortisation formula M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1) was standard textbook material by the late 1800s. American mortgages remained short-term (5-10 years with a balloon repayment) until the Great Depression: in 1933 the Home Owners' Loan Corporation (HOLC) refinanced defaulting mortgages with long-term amortising loans, and in 1934 the Federal Housing Administration (FHA), established by the National Housing Act, insured the long-amortising format that became the modern 30-year fixed-rate mortgage. The other defining piece of US consumer-lending law is the Truth in Lending Act (TILA, 1968), implemented through the Federal Reserve's Regulation Z, which forced lenders to disclose the Annual Percentage Rate (APR) alongside the headline interest rate so borrowers could compare fees-included costs across competing offers. The Consumer Financial Protection Bureau (CFPB), created by the Dodd-Frank Act in 2010 and operational in 2011, took over enforcement of TILA, RESPA, and ECOA, and authored the integrated «Loan Estimate» and «Closing Disclosure» forms now standard for US mortgages. The 30-year fixed-rate mortgage remains the dominant US home loan, and the amortisation formula above is the same one your bank's loan officer uses on her calculator.
The Anatomy of a Loan Payment
- P, the principal. The amount actually being borrowed, after any down payment. On a $400,000 home with an $80,000 down payment, P = $320,000. The full amortisation formula scales linearly with P: double the principal and the monthly payment exactly doubles. Many borrowers accidentally enter the purchase price rather than the loan amount; the difference is the down payment and changes everything downstream.
- r, the periodic interest rate. The annual rate divided by the number of compounding periods per year. For a US monthly mortgage at 6.5% annual, r = 6.5% ÷ 12 ≈ 0.5417% per month. UK mortgages and traditional Canadian mortgages use semi-annual compounding instead, which mathematically makes the effective rate slightly different from a US monthly-compounded loan at the same headline number.
- n, the total number of payments. For a 30-year monthly mortgage, n = 360. For a 5-year auto loan paid monthly, n = 60. Doubling n does not double the total interest paid: extending a 15-year mortgage to 30 years more than doubles total interest, because each dollar borrowed sits on the books twice as long and accrues interest at the higher 30-year rate.
- M, the monthly payment. Computed from the amortisation formula M = P × r(1+r)ⁿ / ((1+r)ⁿ − 1). The payment is fixed for the entire life of a fixed-rate loan, even though the split between interest and principal shifts dramatically over time. The formula assumes equal payments at equal intervals; loans with irregular payment schedules require numerical solution rather than the closed-form expression.
- How each payment splits. Every month's interest equals the previous balance × r. Whatever is left of M after subtracting the month's interest reduces the principal. In month 1 the interest portion is largest because the balance is largest; by the final payment, nearly all of M is principal. The exact split is shown in the amortisation schedule (the table below the results), which is why first-year extra principal payments are so much more powerful than last-year extra payments.
- Total cost = M × n. The grand total you'll pay over the life of the loan. Subtracting the original principal gives the total interest. For the default $250,000 / 6.5% / 30-year mortgage on this page: M ≈ $1,580, total paid ≈ $568,861, total interest ≈ $318,861, well over the original principal. That figure is the real cost of borrowing for thirty years, and it's the number that 15-year-vs-30-year comparisons almost always understate.
Common Loan Types and Who Borrows
- Mortgages (15- and 30-year fixed). The 30-year fixed-rate mortgage is the dominant US home loan, originated through banks, credit unions, and standalone mortgage lenders, often securitised by Fannie Mae, Freddie Mac, or Ginnie Mae. 15-year fixed mortgages carry rates roughly 0.5-0.75 percentage points below their 30-year equivalents and dramatically less total interest, but the monthly payment is around 30% higher. ARM (adjustable-rate) variants like the 5/1, 7/1, and 10/1 fix the rate for an initial period then float.
- Auto loans (36-84 months). Most US auto loans run 60-72 months at 5-9% APR for buyers with average credit, lower for prime borrowers. Longer terms reduce monthly payments but increase the risk of being «underwater» (owing more than the car is worth) for most of the loan. Captive lenders (Ford Credit, Toyota Financial Services, GM Financial, Ally) often beat bank rates with manufacturer-subsidised promotional financing on specific models.
- Student loans (10-25 years). US federal student loans on the Standard Repayment Plan amortise over 10 years. Graduate PLUS and consolidated federal loans can extend to 20-25 years. Income-driven plans (IBR, PAYE, REPAYE, SAVE) modify the monthly payment as a percentage of discretionary income and run longer, with potential forgiveness at the end of the term. Private student loans behave like personal loans and use the amortisation formula identically.
- Personal loans (24-84 months). Unsecured (no collateral) consumer loans from banks, credit unions, and fintech lenders (SoFi, LightStream, Marcus, Discover). Used for debt consolidation, home improvement, or large one-time expenses. Rates run 6-30%+ depending on credit profile, much higher than secured mortgage or auto rates because the lender has no asset to repossess on default and must price in the default risk.
- Home equity loans (5-30 years). A second mortgage against home equity. Fixed-rate, lump-sum, lower rates than personal loans because the home is collateral. Distinct from a HELOC (Home Equity Line of Credit), which is a revolving variable-rate line rather than a fixed-term amortising loan. Home equity loans use the same amortisation formula as a first mortgage.
- Small business loans (1-25 years). SBA 7(a) and 504 loans, conventional commercial bank loans, equipment financing, and merchant cash advances cover a wide range of structures. SBA 7(a) loans run up to 25 years for commercial real estate, 10 years for equipment, and 7 years for working capital. The amortisation formula works the same way; required documentation and personal-guarantee terms differ enormously by lender and loan size.
Standards, Regulations, and Historical Milestones
- Code of Hammurabi (~1754 BCE). Earliest surviving statutory interest caps: 20% per year on silver loans, 33⅓% on grain. Established that lending was a contractual relationship subject to legal limits rather than a private matter between debtor and creditor, and that the state would enforce both sides of the bargain.
- Fibonacci's «Liber Abaci» (1202). Leonardo of Pisa's textbook introduced Hindu-Arabic numerals to Mediterranean Europe and worked out the compound-interest problems that medieval merchants had been computing awkwardly with Roman numerals. The book stayed in print for three centuries and shaped the practical finance of the Italian banking houses.
- Jacob Bernoulli and the constant e (1683). The Swiss mathematician studying the limit of compound interest as the compounding frequency approached infinity discovered the constant e ≈ 2.71828. The number that governs all continuous-compounding finance, and a foundational constant in mathematics generally, emerged out of asking how rich a bank deposit could become.
- Home Owners' Loan Corporation (HOLC, 1933). New Deal agency created in the depths of the Great Depression to refinance defaulting mortgages. Replaced short-term balloon-payment mortgages with the long-term amortising loans that became the modern standard. Also, controversially, created the residential maps that codified redlining.
- Federal Housing Administration (FHA, 1934). Established by the National Housing Act. Insured private long-term amortising mortgages (initially 20-year, later 30-year) with low down payments, transferring default risk from the lender to the federal government. Together with the HOLC, transformed US homeownership from a minority pursuit into a mass-market middle-class entitlement.
- Truth in Lending Act (TILA, 1968) / Regulation Z. Federal law requiring lenders to disclose the Annual Percentage Rate (APR), finance charges, and amount financed before the consumer commits. Implemented through the Federal Reserve's Regulation Z. Made apples-to-apples comparison between loans possible and is the reason every loan document you see contains an APR figure alongside the headline rate.
- Basel Accords (Basel I 1988, II 2004, III 2010). International banking standards on capital adequacy and risk-weighting set by the Bank for International Settlements. Determine how much capital banks must hold against the loans on their balance sheets, which in turn shapes how aggressively lenders originate and price consumer loans across mortgages, auto, and credit-card portfolios.
- Consumer Financial Protection Bureau (CFPB, 2011). Created by the Dodd-Frank Act of 2010 in response to the 2008 financial crisis. Took over enforcement of TILA, RESPA, ECOA, and other consumer-credit laws from the Federal Reserve and other agencies. Operates the integrated «Loan Estimate» and «Closing Disclosure» forms now standard for US mortgage transactions.
More frequently asked questions
How does paying extra principal change the schedule?
An extra principal payment reduces the balance immediately, so the next month's interest is calculated on the smaller balance and more of every subsequent payment goes to principal. The earlier the extra payment, the more total interest it saves. An extra $5,000 in month 1 of a 30-year mortgage typically saves more total interest than four extra $5,000 payments in year 25, because interest accrues on the principal you would otherwise have been carrying for the next 29 years.
Why is my actual monthly mortgage payment higher than this number?
Because lenders typically include property taxes and insurance in the monthly bill via an escrow account: that's the PITI (Principal + Interest + Taxes + Insurance) acronym. Property tax (typically 1-2% of home value annually in the US), homeowner's insurance ($1,000-$3,000 per year), and PMI (if the down payment was below 20%) all add up. The true monthly outlay on a US mortgage is usually 25-40% above the bare P&I figure this calculator returns.
Should I pick a 15-year or a 30-year mortgage?
The 15-year has a lower interest rate (typically 0.5-0.75 percentage points below the equivalent 30-year), much lower total interest, and you own the home outright twice as fast, but the monthly payment is roughly 30% higher. The 30-year frees up cash flow and lets you invest the difference; some financial planners argue this is the better long-term wealth-building choice if you're disciplined enough to actually invest the difference. Run both scenarios in the calculator with realistic rates for each and compare.
Is the calculator accurate for non-US loans?
The amortisation formula is identical worldwide for fixed-rate loans. UK mortgages, Australian home loans, and Canadian variable-rate mortgages all use the same math. The differences are compounding frequency (UK and traditional Canadian mortgages use semi-annual compounding, not monthly), early-repayment penalties, and standard term lengths. The headline monthly payment from this calculator is correct as long as the rate and term you enter match how the loan is structured.
Are my loan figures stored or sent anywhere?
No. The calculator runs entirely in your browser. The loan amount, rate, term, and amortisation schedule are computed and rendered locally. Nothing is transmitted to any server, no analytics events log the values, no marketing list captures your inputs. Loan-shopping data is highly sought-after by lenders and lead-generation companies, and many free calculator sites are funded by selling exactly this information. This one is not.
What is a refinance and when does it make sense?
A refinance replaces your current loan with a new one, typically at a lower rate or different term. The rough rule of thumb: refinancing makes sense if the new rate is at least 0.5-1% below your current rate and you'll stay in the property long enough to recoup the closing costs (usually 2-5% of the loan amount). Use this calculator twice (once with your current loan, once with the refinanced loan) and compare total interest plus closing costs to see whether the math actually works for your situation.