Loan Amortization Calculator

Amortization is the process of paying off a fixed-rate loan through a series of equal periodic payments, where each payment covers the interest owed for that period plus a chunk of the remaining balance. It applies to mortgages, car loans, student loans, personal loans, and any other installment debt with a set term and a fixed rate. This calculator is the generic engine behind that math: enter a principal balance, an annual interest rate, a term in months, and an optional extra monthly payment, and it produces a full period-by-period table plus the four numbers borrowers actually care about: the required monthly payment, the total interest paid over the life of the loan, the total repayment cost, and how much time and money an extra payment saves.

Unlike calculators labeled for a specific loan type (auto, mortgage, student), this one has no built-in tax rates, insurance estimates, or fee assumptions. It is the raw amortization math with nothing added, which makes it the right tool when you already know your principal and rate and just want to see the schedule, or when you want to compare how extra payments affect a loan regardless of what the loan is actually for.

The engine uses the standard fixed-payment amortization formula. For a loan with principal $P$, monthly interest rate $i$ (the annual rate divided by 12), and $n$ total monthly payments, the fixed monthly payment $A$ that fully retires the loan is:

$$A = P \times \frac{i(1+i)^n}{(1+i)^n - 1}$$

Each month, the interest charge is the current balance multiplied by $i$. The remainder of that month's payment reduces the principal, and the new (lower) balance becomes the base for next month's interest charge. This is why early payments are interest-heavy: the balance is still large, so a bigger share of each payment goes to interest. As the balance shrinks, the interest charge shrinks with it, and a growing share of the fixed payment goes to principal.

When an extra payment is added, that amount goes entirely toward reducing principal on top of the scheduled payment. Because interest is always calculated on the current balance, a smaller balance next month means a permanently smaller interest charge every month after that, which is why extra payments save more in total interest than the extra dollars paid alone would suggest, and why they shorten the loan term. The calculator runs this period-by-period simulation to completion, tracking cumulative principal, cumulative interest, and remaining balance at every step, then sums the results to produce total interest and total cost. All arithmetic is performed with decimal-precision math rather than standard floating-point numbers, which avoids the fractional rounding drift that can appear in spreadsheet amortization tables over long schedules.

If the interest rate is entered as 0%, the formula above is undefined (division by zero), so the calculator falls back to simple division: payment equals principal divided by the number of periods, and total interest is zero.

Take a $50,000 loan at 7.50% annual interest for 60 months (5 years), with no extra payment:

1. Monthly rate: $7.50\% / 12 = 0.625\%$, or $i = 0.00625$.
2. Applying the payment formula gives a required monthly payment of $1,001.90.
3. Over 60 payments, total payments come to $60,113.99 (the last payment is adjusted by a few cents to bring the balance to exactly zero).
4. Total interest paid over the full term is $10,113.85, roughly 20% of the original principal.

Now add a $50 extra payment every month on the same loan:

1. The required scheduled payment stays $1,001.90, but the actual monthly outlay becomes $1,051.90.
2. Because extra principal comes off the balance early, the loan is fully paid off in 57 months instead of 60, a 3-month reduction.
3. Total interest drops to roughly $9,515.60, a savings of about $598 compared to the no-extra-payment scenario.

This is the core trade-off the calculator is built to show: a relatively small increase in monthly outflow (here, about 5% more per month) produces a proportionally larger reduction in total interest, because every dollar of extra principal stops accruing interest immediately rather than over the remaining life of the loan.

A useful sanity check case is a 0% loan: a $24,000 balance at 0% interest over 48 months amortizes to an even $500 per month with zero total interest, since there is nothing to compound.

• Origination fees, closing costs, or points. These are separate from principal and are not folded into this generic schedule; loan-specific calculators (mortgage, auto) add fees where relevant.
• Variable or adjustable rates. This calculator assumes one fixed rate for the entire term. Adjustable-rate loans need to be modeled period by period as the rate resets.
• Prepayment penalties. Some loan agreements charge a fee for paying off early or making extra principal payments; check your loan terms before assuming the full projected savings apply.
• Tax deductibility of interest. For loans where interest may be deductible (such as some mortgages), this tool shows the pre-tax interest cost only.
• Payment timing quirks. The schedule assumes payments land exactly on the period boundary with no grace periods, late fees, or day-count adjustments.
• Insurance, taxes, or escrow. For a mortgage specifically, monthly housing costs typically include property tax and homeowners insurance on top of principal and interest; use a mortgage-specific calculator for a full payment estimate.

• Confusing the payment amount with the interest rate. A lower monthly payment doesn't necessarily mean a cheaper loan; a longer term can lower the payment while raising total interest paid.
• Assuming extra payments shorten the term by the same proportion as the extra dollar amount. The relationship is nonlinear because it depends on how much interest was going to accrue on the eliminated balance.
• Applying an extra payment as a principal reduction when the lender actually applies it to a future scheduled payment. Always confirm with your servicer that extra payments are marked "apply to principal," otherwise you may not get the interest savings this schedule projects.
• Comparing two loans by monthly payment alone. A shorter, higher-payment loan often costs far less in total interest than a longer, lower-payment loan for the same principal and rate.
• Forgetting that the interest rate here is the rate applied per period, not an average. A 7.5% annual rate compounded monthly is not the same as paying 7.5% of the principal in interest over the life of the loan; actual total interest depends heavily on the term length.
• Ignoring rounding on the final payment. Because the standard formula produces a level payment that rarely brings the balance to exactly zero, the last payment in a real schedule is almost always a slightly different amount than the rest.

• Truth in Lending Act (Regulation Z), 12 CFR Part 1026: Governs disclosure requirements for consumer credit, including the formulas used to compute annual percentage rate and finance charges.
• Consumer Financial Protection Bureau: Guidance on how amortization works for mortgages and other installment loans, including sample amortization schedules.
• Federal Reserve Board, Regulation Z Official Staff Commentary: Technical basis for standard amortization and finance charge calculations used across U.S. consumer lending.