Loan Payment Calculator
Quickly compute loan payment with accurate formulas. See amortization schedules, growth projections, and side-by-side comparisons.
Calculator
Adjust values & calculateAmortization by Year
Formula
Where M = Monthly payment, P = Principal loan amount, r = Monthly interest rate (annual rate / 12), n = Total number of payments. Total cost = M × n. Total interest = Total cost - P.
Last reviewed: January 2026
Worked Examples
Example 1: Auto Loan Payment
Example 2: Personal Loan Comparison
Background & Theory
The Loan Payment Calculator applies the following established principles and formulas. Finance and investing rest on the foundational concept of the time value of money: a dollar received today is worth more than a dollar received in the future, because present funds can be deployed to earn a return. This principle underlies virtually every valuation technique in modern finance. The future value of a present sum P growing at rate r over n periods is expressed as FV = P(1 + r)^n, while the present value of a future cash flow FV is PV = FV / (1 + r)^n. Compound growth amplifies returns significantly over long horizons, a dynamic often described as the eighth wonder of the world. Net Present Value (NPV) extends these mechanics to evaluate investment projects by summing the present values of all expected cash flows minus the initial outlay: NPV = sum[CF_t / (1 + r)^t] - C_0. A positive NPV indicates the project creates value above the required return. The Internal Rate of Return (IRR) is the discount rate that sets NPV to zero, providing a single percentage benchmark for project comparison. The risk-return tradeoff is the central tension of investment theory. Higher expected returns generally require accepting greater uncertainty. Harry Markowitz formalized this in Modern Portfolio Theory by demonstrating that portfolio variance can be reduced through diversification when assets are imperfectly correlated. The efficient frontier represents the set of portfolios offering the maximum return for a given level of risk. The Capital Asset Pricing Model (CAPM) extends this by introducing the market portfolio as a reference, defining expected return as E(r) = r_f + beta * (E(r_m) - r_f), where beta measures an asset's sensitivity to systematic market risk. Asset classes — equities, fixed income, real assets, and alternatives — differ in their return profiles, liquidity, and correlations. Strategic asset allocation determines long-run target weights based on investor objectives and risk tolerance, while tactical allocation permits short-run deviations to exploit perceived mispricings. Discount rates used in valuation models must reflect the cost of capital appropriate to the risk of the cash flows being discounted, a point stressed in corporate finance texts from Brealey, Myers, and Allen through to Damodaran.
History
The history behind the Loan Payment Calculator traces back through the following developments. The formal practice of lending at interest dates to ancient Mesopotamia, where the Code of Hammurabi around 1750 BCE regulated interest rates on grain and silver loans. Banking as an institutional activity took root in medieval Italy, with merchant bankers in Florence and Venice financing trade across Europe through instruments such as bills of exchange. The Medici family operated one of the most sophisticated banking networks of the fifteenth century, pioneering double-entry bookkeeping and correspondent banking relationships. Organized equity markets emerged in the early seventeenth century. The Dutch East India Company (VOC), chartered in 1602, issued shares to the public and created the Amsterdam Stock Exchange — widely regarded as the world's first formal stock exchange. The VOC allowed investors to buy and sell shares freely, establishing the template for the joint-stock company. The period also produced the Dutch tulip mania of 1636 to 1637, one of history's first recorded speculative bubbles, in which tulip bulb futures contracts reached extraordinary prices before collapsing. England's financial revolution followed in the late seventeenth century with the founding of the Bank of England in 1694 and the development of government bond markets. The South Sea Bubble of 1720 illustrated the dangers of speculative excess and contributed to early securities regulation. Throughout the eighteenth and nineteenth centuries, industrialization created enormous demand for capital, fueling the expansion of stock exchanges in London, Paris, New York, and beyond. The New York Stock Exchange, formalized in 1817, became the world's dominant equities market by the twentieth century. The Great Crash of 1929 and subsequent Great Depression prompted the US Securities Act of 1933 and Securities Exchange Act of 1934, establishing the SEC and mandatory disclosure requirements. Harry Markowitz published his landmark portfolio selection paper in 1952, launching quantitative finance. The CAPM emerged in the 1960s through work by Sharpe, Lintner, and Mossin. John Bogle launched the first retail index fund in 1976, democratizing diversified investing and challenging active management orthodoxy.
Key Features
- Calculate tip amounts and split any restaurant or shared bill evenly among any number of people, including handling unequal splits when individuals order different amounts.
- Compute the final sale price after applying single or stacked discounts, and reverse-calculate the original price from a marked-down amount.
- Determine monthly loan payments given principal, interest rate, and term length, and check whether a payment fits within a target budget as an affordability check.
- Calculate fuel economy in MPG or L/100km, estimate total fuel cost for any road trip by distance and current price per gallon or litre, and find cost-per-mile for vehicle comparison.
- Compare grocery items by unit price across different package sizes and units of measure, instantly identifying the best-value option regardless of how the price is listed.
- Estimate monthly electricity, gas, or water bills by entering appliance wattage and usage hours, helping you identify high-consumption devices and project annual utility costs.
- Convert between major world currencies using a specified exchange rate for quick travel budgeting, and calculate how much local currency you receive after exchange fees.
- Compute percentage increase or decrease between two values, and calculate markup or markdown amounts for pricing decisions or tracking financial changes over time.
Frequently Asked Questions
Formula
M = P[r(1+r)^n] / [(1+r)^n - 1]
Where M = Monthly payment, P = Principal loan amount, r = Monthly interest rate (annual rate / 12), n = Total number of payments. Total cost = M × n. Total interest = Total cost - P.
Worked Examples
Example 1: Auto Loan Payment
Problem: You borrow $25,000 for a car at 7% interest for 5 years. What is your monthly payment and total cost?
Solution: Principal (P) = $25,000\nMonthly rate (r) = 7% / 12 = 0.5833%\nNumber of payments (n) = 5 × 12 = 60\n\nM = $25,000 × [0.005833 × (1.005833)^60] / [(1.005833)^60 - 1]\nM = $25,000 × [0.005833 × 1.4176] / [1.4176 - 1]\nM = $25,000 × 0.008268 / 0.4176\nM = $25,000 × 0.019801 = $495.03
Result: Monthly Payment: $495 | Total Interest: $4,702 | Total Cost: $29,702
Example 2: Personal Loan Comparison
Problem: Compare a $15,000 personal loan at 10% for 3 years vs 5 years.
Solution: 3-year term:\nM = $15,000 × [0.00833 × (1.00833)^36] / [(1.00833)^36 - 1]\nM = $484.01/month\nTotal cost = $484.01 × 36 = $17,424\nTotal interest = $2,424\n\n5-year term:\nM = $15,000 × [0.00833 × (1.00833)^60] / [(1.00833)^60 - 1]\nM = $318.71/month\nTotal cost = $318.71 × 60 = $19,123\nTotal interest = $4,123
Result: 3-year: $484/mo ($2,424 interest) | 5-year: $319/mo ($4,123 interest) — longer term costs $1,699 more
Frequently Asked Questions
How is a loan payment calculated?
Loan payments are calculated using the amortization formula: M = P[r(1+r)^n]/[(1+r)^n-1]. Here, M is the monthly payment, P is the principal (amount borrowed), r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. This formula ensures each payment covers some interest and some principal, with the loan fully paid off after n payments. In the early months, a larger portion goes toward interest. As the balance decreases, more goes toward principal. Loan Payment Calculator works for auto loans, personal loans, student loans, and any fixed-rate installment loan. Understanding this formula helps you compare loan offers and see how rate changes affect your total cost.
What factors affect my loan payment amount?
Three primary factors determine your loan payment: the principal amount, the interest rate, and the loan term. A higher principal means higher payments. A higher interest rate increases both the monthly payment and total interest paid. A longer term reduces monthly payments but increases total interest significantly. For example, a $25,000 loan at 7%: over 3 years costs $772/month with $2,780 total interest; over 5 years costs $495/month with $4,700 total interest; over 7 years costs $378/month with $6,728 total interest. Your credit score heavily influences the interest rate offered — a 720+ score might get 5% while a 620 score might get 12% or more, dramatically changing the cost of borrowing.
Should I pay off my loan early?
Paying off a loan early can save significant money on interest. Extra payments go directly toward the principal, reducing the balance that accrues interest. On a $25,000 loan at 7% for 5 years, adding just $100/month extra saves $1,100 in interest and pays off the loan 13 months early. However, check for prepayment penalties first — some loans charge a fee for early payoff. Also consider opportunity cost: if your loan rate is 4% but you could earn 7% investing, the math favors investing. Prioritize paying off high-interest debt (credit cards, personal loans) before low-interest debt (mortgages, federal student loans). The avalanche method — paying minimums on all debts and extra on the highest-rate debt — saves the most money.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
What inputs do I need to use Loan Payment Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
References
Reviewed by Sahil, Senior Finance & Tax Editor · Editorial policy