Loan Payment Calculator: Amortized Loans Both Ways
Loan Payment Calculator
The standard amortized loan, both directions: from an amount to the payment, or from a payment budget back to the amount it can service. Monthly, biweekly or weekly payments, with the lifetime interest stated plainly, since that is the number the payment quietly hides.
The formula is the annuity identity: payment equals principal times i over 1 minus 1 plus i to the minus n, with i the periodic rate and n the number of payments. Reversing it gives the principal a payment can carry. At long terms most of the early payments are interest, which is why the lifetime interest on a 30 year loan can exceed the amount borrowed.
How to use this tool
Two directions. Give it a loan amount, APR, term and payment frequency, and it returns the payment plus the lifetime totals. Or give it the payment you can afford and it returns the amount that payment services, which is the budgeting question asked the way people actually ask it.
The tool states the total interest plainly, because the payment number hides it: a 300,000 loan at a comfortable-sounding monthly figure quietly costs another 347,000 in interest over thirty years, and that second number belongs in the decision.
One identity, both directions
The standard amortized loan is the annuity identity: payment equals principal times the periodic rate over 1 minus 1 plus the rate to the minus n. Each payment is identical, but its composition shifts: early payments are mostly interest on a large balance, late ones mostly principal, which is why extra payments early in a long loan save disproportionate interest, and why the reverse calculation, principal from payment, is the same formula rearranged rather than a different theory.
One boundary worth respecting: this is the US-style convention where the APR divides evenly into the payment periods. Canadian fixed mortgages compound semi-annually by statute, shifting the payment slightly at the same quoted rate, and lender fees, insurance and rate structure move real quotes further. The tool says so on its face; it is a planning estimate, and the lender document is the number.
A worked check you can repeat on paper
The classic case: 300,000 at 6 percent for 30 years, monthly. The periodic rate is 0.5 percent, n is 360, and the identity gives 1,798.65 a month. Total paid is 647,514.57, so interest is 347,514.57, more than the principal. Feed that payment back into reverse mode at the same rate and term and it returns exactly 300,000, the round trip the tool was verified on, alongside the zero-rate case where 12,000 over one year is simply 1,000 a month.
Mistakes that catch people out
Judging affordability by payment alone. Stretching the term shrinks the payment and swells the interest. Fix: read the lifetime interest line every time the term changes.
Comparing a biweekly quote to a monthly one by multiplying by two. Twenty-six biweekly payments are thirteen months of halves, not twelve. Fix: the frequency selector computes each properly.
Treating this as a mortgage quote. The Canadian compounding convention and lender specifics shift the number. Fix: the warning on the tool is not decoration; confirm with the lender.
How this was checked
The 300,000 case was verified against the annuity identity to ten significant figures, the reverse mode confirmed as its exact inverse on both the mortgage case and a five year vehicle loan, the zero-rate limit checked as simple division, and the biweekly frequency validated against the same engine at 26 periods.
Related Calculators and Reference
The same annuity mathematics running forward, saving instead of borrowing, is the Simple and Compound Interest Calculator. What the payment leaves for everything else is arithmetic for the Percentage Calculator, and the income side of the budget is the Timesheet Duration Calculator. Also see the ROI Calculator: check whether an investment returns more than the loan costs. Also see the Depreciation Calculator: write off an asset bought with the loan. Also see the Mortgage Calculator: a home loan with property tax, insurance and PMI included. Also see the Credit Card Payoff Calculator: how long a card balance takes to clear. Also see the Auto Loan Calculator: the payment on a car loan with sales tax, trade in and fees included. Also see the Debt Payoff Calculator: paying off several loans and cards with one budget. If you are weighing a new rate on an existing loan, the Refinance Calculator finds the break even month. For student loans, which add interest during school and often come in several pieces, the Student Loan Calculator handles several loans, school and grace interest and extra payments.