Loan Amortization Explained: Payments, Interest and Balance

Loan amortization is the process of repaying a loan through scheduled payments that cover interest and reduce the principal over time. This calculator estimates the monthly payment and total interest from the loan amount, annual percentage rate (APR), and term; it assumes equal monthly payments and a fixed rate.

Formula

The calculator uses the standard level-payment loan formula. It finds a payment that, when made every month for the full term, pays both the monthly interest and the amount borrowed:

Payment = round[P × r / (1 − (1 + r)−n), 2]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200. APR is entered as a percentage per year.
• n is the number of monthly payments, calculated as years × 12.
• Payment is the monthly amount, in dollars, rounded to the nearest cent.

Total interest is calculated as Payment × n − P. Since the monthly payment is rounded to cents first, the interest estimate uses that rounded payment, as the calculator does. Actual final payments may differ if a lender adjusts the last amount or uses a different day-count or rounding method.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

1. Convert APR to a monthly rate: 8 ÷ 1,200 = 0.0066667, or about 0.66667% per month.
2. Find the number of payments: 5 × 12 = 60.
3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = $405.53 after rounding to cents.
4. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The estimate is therefore a monthly payment of $405.53 and total interest of $4,331.80 over 60 payments.

Assumptions

• The interest rate is fixed for the whole term.
• Payments are equal, made monthly, and paid at the end of each period.
• Interest is modelled monthly using APR ÷ 12.
• The calculation excludes fees, taxes, insurance, PMI, and escrow. It also assumes no missed payments, extra payments, rate changes, or other balance adjustments.

How Amortization Works

Each payment has two parts: interest charged for the period and principal repayment. Interest is calculated on the outstanding balance. Early in a level-payment loan, that balance is relatively large, so a larger share of each payment generally goes to interest. As principal falls, the interest portion tends to shrink and more of the same payment reduces principal.

For example, in the first month of the default loan, estimated interest is $20,000 × 0.0066667, or about $133.33. From the $405.53 payment, roughly $272.20 reduces principal. The next month’s interest is then calculated on a lower balance. This repeating process is called amortization; the schedule showing each period’s payment, interest, principal, and remaining balance is an amortization schedule.

Amortization is not the same as simply dividing the principal by the number of payments. That division would ignore interest. Nor does a level payment mean the principal portion is level: the total payment stays the same under these assumptions, but its allocation changes over time.

Reading the Estimate and Its Limits

The monthly payment is a principal-and-interest estimate, not necessarily the full amount collected each month. For a mortgage, for instance, taxes, insurance, escrow deposits, or mortgage insurance may be billed alongside the loan payment but are not part of this formula. Fees or a financed charge can also affect the actual amount borrowed or the repayment schedule.

Use the lender’s stated loan amount and APR as inputs, and check whether the APR and repayment terms correspond to the product being evaluated. APR can reflect certain borrowing costs, but this calculator does not separately model fees or reconstruct a lender’s APR. It treats the entered APR as a nominal annual rate divided evenly into monthly periods. A lender may use a different accrual method, payment date, rounding convention, or variable-rate structure.

The estimate also presumes the scheduled payment is made in full each month and that the loan runs for exactly the entered number of months. Extra principal payments, late or skipped payments, deferment, a changing rate, or a different final payment can change both payoff timing and total interest. The calculation is useful for understanding a standard fixed-payment structure, not for predicting every account balance to the cent.

Common Amortization Questions

Does a larger payment reduce total interest?
For a loan with the same rate and no prepayment charges or other adjustments, paying principal faster generally reduces the time interest accrues. This calculator does not model extra payments, so its total-interest result assumes only the scheduled monthly amount.

Why do I pay more interest at the beginning?
Interest for each period is based on the balance at that point. The balance is highest near the start of a fully amortizing loan, so the interest charge is generally larger then. As principal is repaid, the interest portion tends to decline.

Does amortization mean my payment changes?
Not in the fixed-rate, level-payment calculation shown here. The payment stays the same, while the split between interest and principal changes. A variable rate, payment adjustment, or nonstandard loan structure can produce different results.

Why is my lender’s figure different?
The lender may include fees or other charges, use a different APR or term, round at different points, or calculate interest using a different method. Compare the same principal, rate, payment frequency, and repayment period, then refer to the lender’s disclosure for the contract figures.

Can a loan be only partly amortized?
Yes. Some repayment structures leave a balance due at the scheduled end rather than reducing it to zero through equal payments. This calculator assumes full amortization over the selected term and does not calculate a balloon payment or residual balance.

Using the Result Carefully

Small input changes can affect the payment: a longer term spreads repayment across more months, while a different APR changes the interest charged each period. The outputs are mathematical estimates based on the supplied inputs, not a statement of an available rate, a loan offer, or an approval decision. Enter figures from the relevant loan disclosure and account for charges the calculator omits when reviewing the complete payment obligation.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• QuickBooks Term Loan Application: Payment Calculator
• QuickBooks Term Loan Interest Rates and Payments
• QuickBooks Term Loan Payment Calculator

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2