Loan Calculator
Every fixed-rate, fixed-term loan — whether it’s called a personal loan, a student loan, an auto loan, or a mortgage — uses the exact same underlying math to calculate its monthly payment. This calculator applies that universal amortization formula directly to any loan amount, rate, and term, and shows the full month-by-month payment schedule alongside the total interest cost.
How the Loan Calculator Works
Enter a loan amount, an annual interest rate, and a term in years, and the calculator computes the fixed monthly payment using the standard amortizing loan formula. That same payment stays constant for the entire loan, but the split between interest and principal within each payment shifts over time — early payments are mostly interest, later payments are mostly principal, even though the total payment amount never changes.
The Formula Behind Every Amortizing Loan
The monthly payment for a fixed-rate loan is calculated as: payment = P × r ÷ (1 − (1 + r)^−n), where P is the loan principal, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments (years × 12). This single formula, with different inputs plugged in, produces the payment for a $20,000 personal loan, a $400,000 mortgage, or a $30,000 auto loan — the underlying math never changes; only the specific numbers do. Understanding this is useful because it means every amortizing loan calculator on this site, regardless of what it’s specifically named or what extra details it adds (property tax, trade-in value, and so on), is fundamentally running this same core calculation underneath.
Why Early Payments Are Mostly Interest
Interest is calculated fresh each month based on the loan’s current remaining balance, which is largest at the very start of the loan. As the balance gradually decreases with each payment, the interest portion of each subsequent payment shrinks correspondingly, and since the total payment stays fixed, the freed-up amount shifts toward paying down principal instead. This is why a 30-year loan can still have the majority of its balance remaining even after 10 or 15 years of on-time payments — interest consumed the larger share of those earlier payments, with principal reduction accelerating only in the loan’s later years. The Amortization Calculator shows this shifting split explicitly across every single payment for the full loan term, which is a useful way to see this pattern in concrete numbers rather than as an abstract description.
Why Interest Rate Changes the Total Cost More Than People Expect
Because interest compounds against a balance that’s only slowly decreasing, even a seemingly small difference in interest rate produces a meaningfully different total cost over a long loan term. A 1-percentage-point rate difference on a 30-year mortgage, for example, can add tens of thousands of dollars in total interest over the life of the loan — far more than the same rate difference would suggest looking only at the monthly payment change. This is exactly why shopping for the lowest available rate matters disproportionately for longer-term loans, and why even a small rate improvement is worth pursuing on a large, long-term loan specifically.
Specific Loan Types: Where the Extra Details Come In
This calculator handles the pure loan math — principal, rate, term, payment, and interest — without any loan-type-specific additions. Real loans often come with extra factors this general calculator deliberately leaves out, which is exactly why dedicated calculators exist for specific loan types:
- A mortgage adds property tax, homeowner’s insurance, and possibly PMI on top of principal and interest — handled by the Mortgage Calculator.
- An auto loan often involves a trade-in value, sales tax, and dealer fees affecting the actual amount financed — handled by the Auto Loan Calculator.
- A personal loan may carry an origination fee deducted upfront from the funds received — discussed in detail on the Personal Loan Calculator.
- A student loan may have different repayment plan options and deferment considerations beyond the basic fixed-payment structure this calculator assumes.
Use this general calculator to understand or verify the core payment math itself; use the specific calculator for your loan type to account for the additional real-world factors that type of loan typically involves.
Solving in the Other Direction: Payment to Term
This calculator solves for payment given a known term. If instead you know how much you can afford to pay monthly and want to find out how long it would take to pay off a given loan balance at that payment — the reverse calculation — the Payment Calculator handles that direction directly, including a check for whether a chosen payment even covers the loan’s accruing interest.
Finding an Unknown Interest Rate
If you already know the loan amount, term, and monthly payment, but need to determine what interest rate that specific combination implies, the Interest Rate Calculator solves that variation of the same underlying formula, isolating rate instead of payment as the unknown.
Comparing Total Interest Across Loan Terms
A longer loan term reduces the monthly payment but increases total interest paid, since the balance takes longer to decline and therefore accrues interest for a longer period overall. Running the same loan amount and rate through this calculator at a few different term lengths side by side is the clearest way to see that specific trade-off in concrete dollar terms, rather than assessing it from the monthly payment figure alone.
Frequently Asked Questions
What is the formula for a loan payment?
Payment = P × r ÷ (1 − (1 + r)^−n), where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. This single formula applies to every fixed-rate, fixed-term loan regardless of what the loan is specifically for.
Why does a longer loan term mean more total interest, even at the same rate?
Because interest is calculated on the remaining balance each month, and a longer term means that balance takes more months to pay down, giving interest more time to accumulate overall — even though the resulting lower monthly payment can make the longer term feel more affordable.
Why are early loan payments mostly interest rather than principal?
Interest is calculated on the current balance, which is at its highest at the start of the loan. As the balance decreases over time, the interest portion of each fixed payment shrinks, and the remainder shifts toward paying down principal instead.
Is this the same formula used for mortgages, auto loans, and personal loans?
Yes — the core amortization formula is identical across all fixed-rate, fixed-term loans. Loan-specific calculators add extra factors relevant to that loan type (property tax and insurance for mortgages, trade-in value for auto loans, origination fees for personal loans), but the underlying payment calculation is the same one this calculator performs.
How much does a 1% interest rate difference actually matter?
More than it might seem from the monthly payment alone, especially on long-term loans. Because interest compounds against a slowly declining balance over many years, even a 1-percentage-point difference can add up to tens of thousands of dollars in total interest on a large, long-term loan like a mortgage.