Loan Calculator
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A loan payment is not the loan amount divided by the number of months. The lender first converts the annual rate into a monthly rate (annual rate divided by 12); each payment covers that month's interest first, and only the remainder reduces the principal — which is why interest dominates the early payments. With equal installments, total principal plus interest is spread into one fixed monthly payment: payment = P × r × (1+r)^n ÷ ((1+r)^n − 1), where r is the monthly rate and n is the term in months. This page counts in months because personal and auto loans are written that way — 36, 48 or 60 monthly payments — and converting to years first invites an off-by-one-month error; for a mortgage quoted in years, use the mortgage calculator on this site instead.
Three scenarios cover most uses. First, pricing an auto loan: borrow $15,000 at 5% for 36 months and the payment is $449.56 a month with $1,184.28 of total interest; stretch the same loan longer and the payment falls while total interest climbs, so compare the two totals before signing, not just the monthly figure. Second, the term trade-off, which is this page's default example: $20,000 at 6% over 60 months costs $386.66 a month and $3,199.36 in total interest, while a 36-month comparison term costs $608.44 a month and only $1,903.79 in interest — $1,295.57 less interest for $221.78 more each month. A shorter term saves interest when cash flow allows; a longer term protects cash flow when it does not, and the two differences make the trade-off concrete. Third, the payment-to-income check: enter a $6,000 monthly income and the $386.66 payment is 6.4% of it; add other installment payments and regular spending before judging the burden, since the ratio alone says nothing about approval — this page computes the ratio, it does not approve loans.
A few edge cases deserve a clear statement. First, rate basis: enter the nominal annual rate; fees, service charges and insurance are not interest, so the true cost runs above the interest computed here, and on a variable-rate loan actual interest moves with the rate while this page holds the rate fixed. Second, day-count differences: this page uses annual rate ÷ 12 as the monthly rate, while lenders often accrue interest daily, so expect a few dollars of difference plus per-period rounding — that is normal. Third, zero rate: with a 0% annual rate the payment degrades gracefully to principal divided by the number of months. Fourth, input limits: the amount must be above zero, the rate 0–36%, both terms 1–360 months, and an entered income must be above zero — leave income blank to skip the ratio. Fifth, the figures exclude taxes, insurance and fees, and prepayment penalties and rate-reset clauses are out of scope; for a large decision, your loan contract governs.
The page is direct to use: enter the loan amount, annual rate, term in months and comparison term, and the monthly payment, total interest, total cost and payoff date (year-month) calculate as you type; enter an income and the payment-to-income ratio appears too. The comparison section shows the second term's payment and interest with the difference in one line, and the yearly summary shows principal, interest and year-end balance for each year. Copy the result to discuss it with family or a loan officer, and reset returns to the example. Everything runs locally in your browser, and nothing is uploaded.
How to use
- Enter the loan amount, annual rate, term in months and comparison term; the monthly payment, total interest, total cost and payoff date calculate as you type.
- Read the term difference: a shorter comparison term shows how much interest it saves and how much more each month costs; a longer one shows the reverse.
- Enter a monthly income (leave it blank to skip) to see the payment as a share of income.
- Check the yearly summary for each year's principal, interest and year-end balance; copy the result to discuss it, or reset to return to the example.
FAQ
How is the monthly payment calculated?
Divide the annual rate by 12 for the monthly rate r, and take n as the term in months. Payment = P × r × (1+r)^n ÷ ((1+r)^n − 1). Each payment covers that month's interest first and the rest reduces principal; the final payment clears the remaining balance. At a 0% rate the formula degrades to principal divided by months, which this page handles.
Why does a longer term mean a lower payment but more total interest?
Interest is charged on the outstanding balance each month. A longer term spreads principal over more months, so each payment carries less principal and the payment falls — but the balance falls more slowly, so interest is charged for more months and the total rises. A shorter term is the reverse: higher payments, fewer months of interest, a faster-falling balance.
What is the difference between counting in months and counting in years?
The math is the same formula; only the input convention differs. Personal and auto loans are written in monthly installments, so 36 payments means 36 months and entering months cannot slip by one. Mortgages are conventionally quoted in years — use this site's mortgage calculator for those. A five-year loan entered as 60 months gives the same result as five years.
Why does my lender's payment differ by a few dollars?
Three reasons: lenders often accrue interest daily while this page uses annual rate ÷ 12; per-period rounding differs; and a first period shorter than a full month is charged on actual days. Fees, service charges and insurance are also outside this page's interest, so a lender quote that bundles them reads higher. A gap of a few dollars is normal; the loan contract is final.
What payment-to-income ratio is reasonable?
There is no single rule. Housing costs are often judged against a 30–40% band, but that is a housing figure; for a personal loan, add the payment, other installments and regular spending together, and a combined share above half of income calls for a smaller amount or a different term. This page only computes the ratio — approval is the lender's decision.