Understanding how loan payments are calculated helps you evaluate offers, verify your statements, and make informed decisions about extra payments or refinancing. The math applies the same way to mortgages, auto loans, personal loans, and student loans.
The loan payment formula
Monthly payment = P x [r(1+r)^n] / [(1+r)^n - 1], where P is the principal (loan amount), r is the monthly interest rate (annual rate / 12), and n is the total number of payments. For a $20,000 auto loan at 6% APR over 60 months: r = 0.005, n = 60. Monthly payment = $386.66. Understanding the formula shows why the three variables (amount, rate, term) are the only levers available — changing any one changes the payment.
How amortization works
Amortization is the process of paying off a loan through regular equal payments over time. Each payment covers the interest that has accrued since the last payment, and a portion of the principal. Early in the loan, most of each payment goes to interest because the balance is highest. Later in the loan, most goes to principal as the balance shrinks. On a $20,000 loan at 6%: payment 1 covers $100 in interest and $287 in principal. Payment 60 covers roughly $2 in interest and $385 in principal.
How term length affects total cost
Extending the loan term lowers the monthly payment but increases total interest paid. On a $25,000 personal loan at 8%:
36-month term: $783/month, about $3,200 total interest.
60-month term: $507/month, about $5,400 total interest.
84-month term: $390/month, about $7,800 total interest.
The 84-month loan saves $393/month compared to the 36-month loan but costs $4,600 more in total interest. Whether the monthly savings are worth the additional total cost depends on how tight the monthly budget is.
When extra payments make sense
Extra payments applied to principal reduce both the remaining balance and future interest. On a $20,000 auto loan at 6% with 48 months remaining, an extra $100/month toward principal pays off the loan about 8 months early and saves roughly $450 in interest. Before making extra payments, confirm your loan has no prepayment penalty, and confirm that extra payments are being applied to principal rather than held as a prepaid future payment.
Frequently asked questions
What is the difference between a fixed-rate and variable-rate loan?
Fixed-rate loans have a rate that does not change — your payment is the same every month. Variable-rate loans have a rate tied to a market benchmark that can rise or fall, changing your payment over time. Most personal and auto loans are fixed-rate. HELOCs and some student loans are variable.
Does paying bi-weekly instead of monthly save money?
Yes, on loans that allow it. Making half the monthly payment every two weeks results in 26 half-payments per year — equivalent to 13 full monthly payments instead of 12. The extra payment per year accelerates payoff and reduces total interest. Confirm your lender applies the extra payments correctly.
Sources and review notes
WalletCalcs uses official consumer finance, tax, labor, and banking references where possible. These links support the general educational guidance on this page;.