Loan Amortization Calculator

The monthly payment (M) for a fixed-rate loan is calculated using the standard amortization formula: M = P * [r(1+r)^n] / [(1+r)^n – 1], where P is the principal loan amount (the amount borrowed), r is the monthly interest rate (the annual percentage rate APR divided by 12, expressed as a decimal, e.g., 6% APR = 0.06/12 = 0.005), and n is the total number of monthly payments (loan term in years multiplied by 12). This formula derives from the present value of an annuity, ensuring that each payment covers the interest accrued during the month and reduces the principal such that the loan balance reaches zero after n payments. The total interest paid is calculated as (M * n) – P, and the total cost is M * n. The formula is mathematically correct because it solves for the constant payment that equates the sum of discounted future payments to the initial principal, using the geometric series formula. It assumes a fixed interest rate and equal payment intervals, which is standard for most mortgages, auto loans, and personal loans.

A 'good' monthly payment is one that fits comfortably within your budget—generally no more than 28-36% of your gross monthly income for housing loans, or 10-15% for other debt. The total interest cost depends heavily on the APR and term: a lower APR and shorter term minimize total interest, but increase monthly payments. A longer term reduces monthly payments but dramatically increases total interest. For example, a 30-year mortgage at 6% on $200,000 yields about $231,000 in total interest, while a 15-year term at the same rate yields about $104,000. Interpret the total cost as the true price of borrowing—compare it to the principal to gauge the loan's cost. There is no universal 'good' number; it depends on your cash flow, loan purpose, and alternative uses of money. Generally, aim for the shortest term you can afford without straining your budget, and shop for the lowest APR based on your creditworthiness.

A common mistake is confusing APR with the monthly interest rate—forgetting to divide by 12 leads to grossly overestimated payments. Another error is using the nominal annual rate instead of the periodic rate when payments are more frequent than monthly (e.g., bi-weekly). People also mistakenly assume the formula accounts for fees or variable rates; it does not—this is for fixed-rate loans only. Edge cases include extremely low APRs (near 0%), where the payment approaches principal divided by n, and very high APRs (e.g., 36% on payday loans), where interest dominates early payments. Another pitfall is rounding too early in calculations, which can shift the final payment by dollars; always keep high precision until the end. Finally, some borrowers think the total interest is simply APR times principal times term, ignoring amortization—this is incorrect because interest is only charged on the remaining balance.

Principal

The initial amount of money borrowed, excluding interest and fees.

Annual Percentage Rate (APR)

The yearly interest rate charged on a loan, expressed as a percentage, including any fees or costs.

Amortization

The process of gradually paying off a loan through scheduled payments that cover both interest and principal.

Monthly Payment

The fixed amount paid each month to satisfy the loan terms, calculated to fully repay the loan by the end of the term.

Total Interest

The cumulative amount of interest paid over the entire loan term, equal to total payments minus the principal.