Loan Repayment Amortization Calculator: Payments and Interest

A loan repayment amortization calculator estimates the fixed monthly payment and total interest for a fully amortizing loan. Enter the loan principal, annual percentage rate (APR), and term in years to see the payment and the interest paid across the scheduled term.

Formula

The calculator treats the loan as a series of equal monthly payments. The payment is the principal multiplied by the monthly interest rate, divided by one minus the growth factor for the full number of payments:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1,200. For an 8% APR, r = 0.08 ÷ 12.
• n is the total number of monthly payments: years × 12.

Total interest is calculated as monthly payment × n − P. The displayed payment is rounded to cents, and the total-interest calculation uses that displayed rounded payment. This makes the estimate easy to follow, although a lender may handle the final payment or rounding differently.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a five-year term.

1. Convert the APR to a monthly decimal rate: 8 ÷ 1,200 = 0.0066667.
2. Find the number of payments: 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] ≈ $405.53 per month.
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 remains fixed for the entire term.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest compounds monthly using APR divided by 12.
• The calculation excludes fees, taxes, insurance, PMI, escrow, and other charges unless they are included in the principal entered.

What Amortization Shows

Amortization is the gradual repayment of a loan through scheduled payments. Each payment covers interest accrued for the period and reduces principal. Early in a typical fully amortizing loan, the outstanding balance is relatively large, so more of a payment goes toward interest. As principal falls, the interest portion usually declines and the principal portion rises.

The payment formula balances those changing portions so that, under its assumptions, the scheduled payments repay the principal and interest by the end of the term. A calculator’s payment figure is not necessarily the amount due on a lender statement: the statement may include charges, a different payment schedule, or adjustments not represented here.

How to Use and Read the Results

Use the original amount borrowed as the loan amount, rather than the total of all future payments. Enter the APR as a percent per year, such as 8 for 8%, not 0.08. Enter the term in years; the calculator converts it into monthly payments. The inputs allow an APR from 0.01% to 100% and a term from 0.0833 to 50 years.

• Monthly payment is the calculated scheduled payment for principal and interest.
• Total interest is the estimated interest across the full stated term, based on the rounded monthly payment.

To compare scenarios arithmetically, change one input at a time and observe how the outputs change. A longer term generally spreads repayment over more monthly payments; the payment and total interest respond to both the term and the rate. These calculations do not determine whether a loan is suitable or whether a borrower qualifies. Obtain the actual rate, fees, payment schedule, and other terms from the lender.

Common Questions and Limits

A frequent misunderstanding is that the monthly payment multiplied by the number of months is the amount borrowed. That product is the total of scheduled payments, which includes principal and interest. In this example, $405.53 × 60 is $24,331.80; subtracting the $20,000 principal gives $4,331.80 in estimated interest.

The formula models fixed-rate, equal monthly payments on a fully amortizing loan. It does not model variable rates, interest-only periods, balloon payments, skipped or late payments, payment changes, daily interest calculations, or extra principal payments. Extra payments can change the balance and payoff timing, so this calculator’s scheduled-term total will not describe that altered schedule.

Rounding matters. The formula shows a payment to the nearest cent, while a loan servicer may calculate interest at more detailed precision and adjust the final payment. The calculator also treats APR as the rate used in its monthly-interest formula; it does not separately itemize lender charges or calculate a fee-adjusted borrowing cost.

Frequently Asked Questions

What does an amortization calculator calculate?
It estimates a recurring payment that repays a stated principal and interest over a specified term, along with total interest under the selected assumptions.

Does the monthly payment include taxes and insurance?
No. The result covers principal and interest only. Taxes, insurance, escrow, PMI, and fees are not included unless represented in the amount entered, and combining them into principal changes what the estimate means.

Why does a longer loan term affect total interest?
A longer term means more payment periods. Even if the scheduled monthly payment is lower, interest is calculated over more periods, so the total-interest estimate may be higher.

Can I use this for a variable-rate loan?
Not as a full repayment forecast. The calculator assumes one fixed APR for the entire term; a changing rate requires recalculating the payment and balance as the rate changes.

Why might my lender’s payment differ?
The lender may use different rounding, timing, fees, payment dates, or loan terms. Check the lender’s disclosure for the actual scheduled amount and included charges.

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

Related

• Commercial Loan Amortization Calculator and Payment Schedule
• Business Loan Amortization Calculator and Payment Formula
• Car Loan Amortization: Payments, Interest, and Balance

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 | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2