Last updated: August 21, 2026
Loan Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
A loan payment is calculated using the standard amortization formula M = P × r(1+r)^n / ((1+r)^n − 1), where P is the principal, r is the periodic interest rate (APR divided by payment periods per year), and n is the total number of payments. For zero-interest loans, the payment simplifies to M = P / n. This free calculator supports monthly, bi-weekly, and weekly payment frequencies and shows how extra payments reduce total interest and payoff time.
The loan payment formula is M equals P times r times (1 plus r) to the power n, divided by (1 plus r) to the power n minus 1, where P is the principal, r is the periodic interest rate, and n is the total number of payments.
Key Takeaways
- Use M = P × r(1+r)^n / ((1+r)^n − 1) to calculate any fixed-rate loan payment; at 0% APR use M = P / n
- Bi-weekly payments reduce a 30-year mortgage by 4–5 years by making one extra annual payment
- Extra payments go directly to principal, cutting all future interest charges on that amount
- Always compare loans using APR (which includes fees), not the nominal interest rate alone
- Shorter loan terms cost less in total interest even though monthly payments are higher
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
M = P × r(1+r)^n / ((1+r)^n − 1)
Where:
- M=Periodic Payment(USD)
- P=Principal Loan Amount(USD)
- r=Periodic Interest Rate (APR / periods per year)(decimal)
- n=Total Number of Payments(periods)
Worked Examples
Personal Loan — 3-Year Term
Financing a $10,000 personal loan at 7% APR for 36 months with monthly payments
- 1Monthly rate r = 7% / 12 = 0.58333%
- 2Total periods n = 3 × 12 = 36
- 3Payment factor = r(1+r)^36 / ((1+r)^36 - 1) = 0.030877
- 4Monthly payment M = $10,000 × 0.030877 = $308.77
- 5Total paid = $308.77 × 36 = $11,115.75
- 6Total interest = $11,115.75 - $10,000 = $1,115.75
Home Mortgage — 30-Year Fixed
Financing a $250,000 mortgage at 6.5% APR for 30 years with monthly payments
- 1Monthly rate r = 6.5% / 12 = 0.54167%
- 2Total periods n = 30 × 12 = 360
- 3Payment factor = r(1+r)^360 / ((1+r)^360 - 1) = 0.006321
- 4Monthly payment M = $250,000 × 0.006321 = $1,580.17
- 5Total paid = $1,580.17 × 360 = $568,861.22
- 6Total interest = $568,861.22 - $250,000 = $318,861.22
Zero-Interest Loan — 24 Months
Financing $5,000 at 0% APR (promotional financing) over 24 months
- 1APR = 0% — standard formula divides by zero, so use equal principal payments
- 2Monthly payment M = $5,000 / 24 = $208.33
- 3Total paid = $208.33 × 24 = $5,000.00
- 4Total interest = $0.00
Introduction
A loan calculator lets you instantly compute your periodic payment, total interest, and payoff schedule for any type of loan — personal loans, auto loans, student loans, or mortgages. Using the standard amortization formula M = P × r(1+r)^n / ((1+r)^n − 1), where P is the principal, r is the periodic interest rate, and n is the total number of payments, this tool gives you accurate results in seconds. Understanding these numbers before you borrow empowers you to compare loan offers, minimize lifetime interest costs, and avoid payment shock.
How the Loan Payment Formula Works
The standard amortization formula M = P × r(1+r)^n / ((1+r)^n − 1) is used by every lender worldwide. P is the principal (the amount borrowed), r is the periodic rate (annual APR divided by the number of periods per year), and n is the total number of payment periods. Each payment covers the month's accrued interest first; the remainder reduces the principal. Because the outstanding balance shrinks each period, the interest portion of each payment gradually decreases while the principal portion increases — a process called amortization. In the first month of a 30-year mortgage, over 90% of the payment may be interest; in the final month, almost all is principal. Pair this calculator with our amortization calculator to view the full payment schedule.
- P — Principal:
the original borrowed amount before any interest accrues
- r — Periodic rate:
APR ÷ 12 for monthly, APR ÷ 26 for bi-weekly, APR ÷ 52 for weekly
- n — Total periods:
term in years × periods per year
- M — Periodic payment:
constant throughout the loan (for fixed-rate loans)
Zero-Interest Loans and the Edge Case
When the APR is 0%, the standard formula produces a division-by-zero error because the denominator (1+r)^n − 1 equals zero. The correct solution is simple: when there is no interest, each payment is just the principal divided equally across all periods: M = P / n. This situation arises with promotional 0% financing, interest-free installment plans, and some family or employer loans. Our calculator automatically detects a 0% rate and applies this fallback, so you always get a mathematically correct result. For any positive interest rate — even 0.01% — the full amortization formula is applied.
How Payment Frequency Affects Total Interest
Switching from monthly to bi-weekly payments is one of the most powerful — and underused — debt reduction strategies. With bi-weekly payments, you make 26 half-payments per year (equivalent to 13 monthly payments) instead of 12. That one extra annual payment directly reduces the principal, compressing the loan term and cutting total interest significantly. On a $250,000 mortgage at 6.5% APR for 30 years, bi-weekly payments can shave about 4–5 years off the term and save tens of thousands in interest. Weekly payments produce a similar — though slightly smaller — benefit compared to bi-weekly. This calculator supports all three frequencies so you can see the exact difference for your specific loan.
- Monthly:
12 payments/year — standard, lowest payment amount
- Bi-Weekly:
26 payments/year — equivalent to 13 monthly payments annually
- Weekly:
52 payments/year — maximum interest reduction, smallest individual payment
The Power of Extra Payments
Making even a small extra payment each period can dramatically reduce the lifetime cost of a loan. The extra amount goes directly to principal (not interest), which reduces every future interest charge. On a $10,000 personal loan at 7% APR for 36 months, adding just $100 per month reduces the payoff to 27 months and saves $294.41 in interest — a 26% reduction. The effect is even larger for longer-term loans: adding $200/month to a 30-year mortgage can cut the term by over 6 years. Our calculator computes both the standard payoff schedule and the accelerated schedule side-by-side, showing you the exact months saved and interest saved.
Which Loan Types This Calculator Covers
This general-purpose loan calculator applies to any fixed-rate, fully amortizing loan. Common uses include:
Personal loans — unsecured installment loans from banks, credit unions, or online lenders
Auto loans — vehicle financing (also try our dedicated auto loan calculator)
Student loans — federal and private education financing
Home equity loans — lump-sum loans secured by home equity
Small business loans — fixed-rate term loans for business financing
Personal lines of credit — when drawn as fixed-term installment loans
APR vs. Interest Rate: What to Enter
Many borrowers confuse the nominal interest rate with the APR (Annual Percentage Rate). The interest rate is the pure cost of borrowing the principal, expressed annually. The APR includes the interest rate PLUS most fees — origination fees, mortgage points, and certain closing costs — expressed as an annual rate. For calculating payment amounts, lenders use the nominal interest rate (not APR). However, for comparing two loan offers from different lenders, always compare APRs because they capture the true total cost including fees. When a lender quotes you an APR, use that figure in this calculator for the most accurate total cost comparison. For mortgages, the difference between the interest rate and APR can be 0.2–0.5 percentage points due to points and fees.
How Much Loan Can You Afford?
Lenders use the debt-to-income ratio (DTI) to assess whether you can afford a loan. DTI = total monthly debt payments / gross monthly income. Most lenders require a DTI below 43% for mortgages and below 36% for personal loans. A common rule of thumb is to keep total debt payments below 36% of gross income. For example, on a $60,000/year gross income (=$5,000/month), total monthly debt should stay below $1,800. If you already have a $400/month car payment, you have about $1,400 remaining for a new loan payment. Use our debt-to-income ratio calculator to check your current ratio before applying.
Quick Reference Card
Loan Calculator Quick Reference
Quick reference • Loan Calculator
M = P × r(1+r)^n / ((1+r)^n − 1) | Zero APR: M = P / nValid range: Principal > 0; APR ≥ 0%; Term ≥ 1 month
Common Values
⚠ Watch Out
- •APR includes fees; nominal interest rate does not — use APR for comparisons
- •Variable-rate loans cannot be accurately modeled with this fixed-rate formula
- •Some lenders compute interest on a 360-day year; results may differ slightly
- •Balloon payment loans have a different structure — regular formula does not apply
Pro Tips
- →Add even $50/month extra on a mortgage to save thousands over the loan life
- →Bi-weekly payments are the easiest way to make one extra payment per year without changing your budget
- →Compare APRs (not interest rates) when shopping multiple lenders
- →Request a full amortization schedule from your lender to see how early payments reduce principal
FAQs
What is the standard loan payment formula?
The standard amortization formula is M = P × r(1+r)^n / ((1+r)^n − 1), where M is the periodic payment, P is the principal (loan amount), r is the periodic interest rate (APR divided by the number of payment periods per year), and n is the total number of payments. This formula assumes a fixed interest rate and equal payments throughout the loan term.
How is monthly interest calculated on a loan?
Monthly interest is calculated by multiplying the outstanding loan balance by the monthly interest rate. For example, if you owe $10,000 at 7% APR, the monthly rate is 7% / 12 = 0.5833%, so the first month's interest is $10,000 × 0.005833 = $58.33. The remainder of your payment reduces the principal. This process repeats each month on a lower balance — called amortization.
What happens at 0% interest rate?
When the APR is 0%, the standard formula produces a division by zero because the denominator becomes zero. The correct approach is to divide the principal equally across all payment periods: M = P / n. For a $5,000 loan at 0% APR over 24 months, the payment is $5,000 / 24 = $208.33 per month with zero total interest. Our calculator applies this fallback automatically.
Does paying bi-weekly instead of monthly save money?
Yes — significantly. With bi-weekly payments, you make 26 half-payments per year, which equals 13 full monthly payments instead of 12. That extra payment each year goes straight to principal, shortening the loan term and reducing total interest. On a 30-year mortgage, bi-weekly payments typically cut the term by 4–5 years and can save tens of thousands of dollars in interest.
How much interest will I save with extra payments?
Every extra dollar of principal payment eliminates all future interest that would have been charged on that dollar. The savings compound over time. For a $10,000 loan at 7% APR over 36 months, adding just $100 extra per month saves $294.41 in interest and pays off the loan 9 months early. For longer-term loans like mortgages, the savings are much larger because interest accrues over more years.
What is the difference between APR and interest rate?
The interest rate is the cost of borrowing the principal, expressed as an annual percentage. The APR (Annual Percentage Rate) includes the interest rate plus most lender fees (origination fees, mortgage points, closing costs), expressed as a single annual rate. Always compare APRs when evaluating loan offers because it captures the true total cost. Use the nominal interest rate for payment calculations; use APR for comparing competing loan offers.
Can I use this for mortgage calculations?
Yes. Enter the mortgage principal, annual interest rate (note: this is the nominal rate, not the APR), and 30 (or 15) years as the term. Select monthly or bi-weekly payment frequency. The calculator gives you the payment, total interest, and — if you enter an extra payment — the months you will save. For a full month-by-month amortization table, use our dedicated amortization calculator.
How does loan term length affect total interest paid?
Longer terms lower the monthly payment but dramatically increase total interest paid. For a $10,000 loan at 7% APR: a 3-year term costs $1,115.75 in interest; a 5-year term costs $1,879.50 in interest — 68% more despite only a 67% longer term. This is because interest accrues on the higher remaining balance for longer. Choosing the shortest term you can comfortably afford minimizes lifetime borrowing cost.