Loan Calculator
✦ Finance & MoneyUse this loan calculator to find your monthly payment, total interest and payoff date — or enter a target payment to see how much you can borrow or how quickly you can be debt-free, with an extra-payment accelerator.
- ✓ Calculated in your browser
- ✓ Nothing you type is stored
- ✓ No sign-up required
- ✓ Formula and sources shown
The formula
Level-payment formula — three solve directions
Payment: M = P × [r(1+r)^n] / [(1+r)^n − 1] | Amount: P = M × [(1+r)^n − 1] / [r(1+r)^n] | Term: n = −ln(1 − P·r/M) / ln(1+r)P = loan amount; M = monthly payment; r = annual rate / 1200 (monthly rate); n = term in months. Rounding: M rounded to the cent; interest each period computed on the unrounded balance; the final payment absorbs the rounding residual. Period model — not an actual-days calculation. No fees, taxes or program rules: those are what the type-specific pages add.
Calculating it by hand
- Choose a solve mode: Payment (default), Borrowing amount or Loan term.
- Enter the loan amount (or leave it for the calculator to solve if you chose Amount mode).
- Enter the annual interest rate — illustrative default is shown; enter your actual rate.
- Enter the loan term in years or months (or leave it for Term mode).
- In Amount or Term mode, enter the target monthly payment you can afford.
- Open Advanced to add an extra monthly payment and see how much interest it saves.
Worked examples
$10,000 at 7% for 5 years (monthly)
r = 0.07 / 12 = 0.005833n = 5 × 12 = 60(1.005833)^60 = 1.41760M = 10000 × 0.005833 × 1.41760 / (1.41760 − 1)M = 10000 × 0.008270 / 0.41760 = $198.01Total paid = 59 × $198.01 + a final $198.15 (the last payment absorbs the rounding residual) = $11,880.74Total interest = $11,880.74 − $10,000 = $1,880.74
Monthly payment: $198.01 | Total interest: $1,880.74 | Total paid: $11,880.74
Solve for amount: $300/mo at 6% for 48 months
r = 0.06 / 12 = 0.005n = 48(1.005)^48 = 1.27049P = 300 × (1.27049 − 1) / (0.005 × 1.27049)P = 300 × 0.27049 / 0.0063525 = 300 × 42.580 = $12,774.10
Borrowing amount: $12,774.10 at $300/month (total interest $1,625.91)
Solve for term: $15,000 at 8% paying $350/month
r = 0.08 / 12 = 0.006667P·r = 15000 × 0.006667 = $100.00 (first month interest)1 − P·r/M = 1 − 100/350 = 0.71429n = −ln(0.71429) / ln(1.006667)n = 0.33647 / 0.006645 = 50.6 → 51 months
Loan term: 51 months (4 years 3 months)
Methodology
How loan payments are actually calculated
The monthly payment formula is simple — but the three questions people actually ask run in different directions: payment, borrowing amount and time. Most calculators only answer the first one.
Read sources and limitsHow do you calculate your monthly loan payment?
A standard instalment loan uses the level-payment formula: M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12 ÷ 100), and n is the total number of monthly payments. The result is the fixed payment that retires the loan in exactly n months.
For example, a $10,000 loan at 7% for 5 years: r = 0.07 / 12 = 0.005833; n = 60; (1.005833)^60 = 1.41760; M = 10,000 × 0.005833 × 1.41760 / (1.41760 − 1) = 10,000 × 0.008270 / 0.41760 = $198.01. This calculator rounds to the nearest cent, computes interest each period on the unrounded balance, and has the final payment absorb the rounding residual — exactly how lenders calculate.
How much can you borrow for a given monthly payment?
The algebraic inverse is: P = M × [(1+r)^n − 1] / [r(1+r)^n]. If you can afford $300 a month, want a 4-year loan and the rate is 6%, then r = 0.005, n = 48, and P = 300 × (1.005^48 − 1) / (0.005 × 1.005^48) = 300 × 0.27049 / 0.0063525 ≈ $12,774.
This mode lets you work backwards from a budget. Instead of starting with a loan amount and seeing whether the payment fits, you start with what you can afford each month and find out what loan it supports at your rate and term. Use it before approaching a lender to understand your ceiling before hearing theirs.
How long will a loan take to repay at a given payment?
Rearranging the formula for n: n = −ln(1 − P·r/M) / ln(1+r). If you owe $15,000 at 8% and can pay $350 a month: r = 0.006667; P·r = 15000 × 0.006667 = $100 (first month interest); 1 − 100/350 = 0.71429; n = −ln(0.71429) / ln(1.006667) = 0.33647 / 0.006645 ≈ 50.6 → 51 months.
There is one guard on this mode: your payment must exceed the first period's interest. If P × r / 12 ≥ M, the loan can never be repaid — each payment only covers part of the interest and the balance grows. This calculator catches this case and returns a plain-English error message rather than an impossible number.
Why does a small extra payment save so much interest?
Any amount paid above the scheduled payment reduces the outstanding balance. Because next month's interest is calculated on that lower balance, a smaller slice of the next payment goes to interest and a larger slice reduces principal. This compounding effect means every early extra dollar saves more than a late extra dollar of the same size.
On a $10,000 loan at 7% for 5 years, paying $50 extra per month cuts total interest from $1,880.74 to $1,433.87 — a saving of $446.87, nearly nine months of the extra payments themselves. It also shortens the term by 13 payments — 47 instead of 60. Enter your loan in this calculator and try $50 in the Extra payment field to see the exact saving on your numbers.
What does this loan calculator not include?
This is the plain loan calculator: amount, rate, term, optional extra payment. It deliberately excludes fees, taxes, insurance, PMI and loan-program rules because those are what the type-specific calculators add, and mixing them into one tool would require six or more additional inputs that most users do not need.
If you are buying a home, use the Mortgage Calculator for PITI (principal, interest, taxes and insurance) and the House Affordability Calculator to find your maximum purchase price. If you are buying a car, use the Auto Loan Calculator for trade-in, sales tax and negative equity. For a loan with an origination fee, use the APR Calculator to find the true cost. To see the full month-by-month schedule with bi-weekly, weekly and quarterly frequencies, use the Loan Amortization Calculator.
Loan questions
How much will my loan payment be?
Your monthly payment depends on three things: the loan amount, the annual interest rate and the term in months. The formula is M = P × [r(1+r)^n] / [(1+r)^n − 1], where r is the monthly rate and n is the number of payments. Enter your figures in the Payment tab above and the answer updates instantly. For a $10,000 loan at 7% for 5 years, for example, the monthly payment is $198.01.
What is the monthly payment on a $25,000 loan?
It depends on the rate and term. At 6.5% for 5 years the payment is $489.15 (total interest $4,349). At 7% for 5 years it is $495.03 (total interest $4,702). At 6.5% for 3 years the payment is $766.23 (total interest $2,584). Enter the rate you have been quoted for the exact figure.
How much can I borrow for $500 a month?
Switch to Borrowing amount mode, enter $500 as the target payment, your interest rate and the term. At 7% for 5 years a $500 monthly payment supports a loan of about $25,251. At 7% for 3 years, the same payment supports about $16,193. The longer the term, the more you can borrow for the same monthly outlay — but the more you pay in total interest.
How do I calculate my loan payment by hand?
Four steps: (1) Divide the annual rate by 12 to get the monthly rate r. (2) Raise (1 + r) to the power of the term in months n. (3) Multiply the result by r, then divide by [(1+r)^n − 1]. (4) Multiply by the loan amount P. The worked examples on this page show the arithmetic step by step.
What is the difference between this loan calculator and a mortgage calculator?
This calculator handles any plain instalment loan: amount, rate, term, optional extra payment. It deliberately omits fees, property taxes, homeowners insurance, PMI and loan-program rules. The Mortgage Calculator adds all of those to give you a full PITI payment. Use this page to understand the core payment maths; use the Mortgage Calculator when you are planning a home purchase.
Does paying extra each month really save much interest?
Yes — and the effect is largest in the early months when your balance is highest. On a $25,000 loan at 6.5% for 5 years, paying $100 extra per month saves about $865 in interest and shortens the term by 11 payments. The saving shrinks if you start the extra payments late. Try the Extra payment field in the Advanced panel to see the exact impact on your loan.
What is total interest on a loan?
Total interest is the sum of the interest portion of every payment over the life of the loan. It equals total paid minus the loan amount. In the early months of an amortising loan, most of each payment goes to interest and little to principal. As the balance falls, this ratio reverses. The Loan Amortization Calculator shows the exact split for every single payment.
What does this calculator not include?
Origination fees (use the APR Calculator), property taxes and insurance (use the Mortgage Calculator), sales tax and trade-in credits (use the Auto Loan Calculator), in-school interest accrual (use the Student Loan Calculator), and any government loan-program rules (use FHA, VA, USDA or Conventional Mortgage calculators). This is the plain-maths page: the formula and nothing else.
Source notes
Method, sources & limitations
Every figure on this page comes from the formula above applied to the values you enter. Nothing is estimated from market data, and no result is a forecast. These are the sources behind the method and any fixed figures it uses:
- CFPB — What is an amortization schedule?
- Federal Reserve — Consumer's Guide to Mortgage Refinancing
- 12 CFR §1026.18 (Regulation Z) — closed-end credit disclosures: amount financed, finance charge, payment schedule
- CFPB — What is the difference between a loan's interest rate and its APR?
Educational information only. Results are estimates produced from the assumptions you enter, and are not financial, tax, legal or medical advice. Check anything that matters against a qualified professional and the cited sources.