Personal Loan Calculator Monthly Amortization Formula

A personal loan calculator uses the monthly amortization formula to estimate a fixed monthly payment from the loan amount, annual percentage rate (APR), and term. Enter those three figures to see the payment and estimated total interest; the calculation assumes equal monthly payments and a fixed rate.

Formula

The monthly payment is the loan principal multiplied by the monthly interest rate, divided by one minus the present-value factor for all payments:

Payment = P × r / [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal. With APR entered as a percentage per year, r = APR / 1200. For example, 8% APR gives r = 8 / 1200.
• n is the total number of monthly payments. For a term in years, n = years × 12.

The calculator rounds the resulting monthly payment to cents. It estimates total interest as the rounded payment multiplied by the number of months, minus the original principal: Total interest = payment × n − P. Because this second calculation uses the displayed rounded payment, it reflects the same payment amount shown above.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and 5 years—the calculation has these steps:

1. Convert APR to a monthly decimal rate: r = 8 / 1200 = 0.0066666667.
2. Convert the term to monthly payments: n = 5 × 12 = 60.
3. Substitute into the formula: payment = 20,000 × 0.0066666667 / [1 − (1 + 0.0066666667)⁻⁶⁰].
4. The unrounded result is about $405.528; rounded to cents, the monthly payment is $405.53.
5. Estimate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The final payment may differ slightly from the regular payment because real lenders can adjust the last amount to account for exact payment dates, rounding, or other contract details.

Assumptions

• The interest rate stays fixed for the full loan term.
• Payments are equal, made monthly, and paid at the end of each period.
• Interest accrues monthly using APR divided by 12.
• The estimate excludes origination or other fees, taxes, insurance, PMI, and escrow; none are inputs in this calculator.

How Monthly Amortization Works

Amortization divides repayment into scheduled installments that cover both interest and principal. In a typical fixed-rate calculation, interest for a month is based on the unpaid balance. The part of that month’s payment left after interest is applied reduces the balance.

At the start, the balance is larger, so more of each payment goes toward interest. As the balance declines, the interest portion generally shrinks and more of the same payment reduces principal. The payment formula sets the amount so the balance reaches zero after n payments under its assumptions. This is why a longer term usually lowers the required monthly payment but can increase total interest: the debt remains outstanding for more periods.

How to Use and Read the Estimate

Use the amount you expect to borrow, the APR supplied for the specific loan offer, and the scheduled term. APR is entered as a percentage per year, not as a decimal: enter 8 for 8%, not 0.08. The calculator converts it to a monthly rate internally. If the lender quotes a different term or rate, enter those figures to produce a separate estimate rather than treating this example as an offer.

• Monthly payment is the regular principal-and-interest amount under the model.
• Total interest is the estimated amount paid above the original principal across the scheduled payments.

These figures do not show every possible amount due at signing or during repayment. Review a lender’s written disclosure and payment schedule for the actual payment dates, fees, and total cost.

Common Mistakes and Formula Limits

A frequent error is mixing rate units. The formula requires a monthly decimal rate, so an APR entered as a whole-number percentage must be divided by 1200. Dividing by 100 gives an annual decimal rate, which is not the monthly rate required here. Another common error is using months as though they were years: a five-year term is 60 payments, not five.

Rounding can also cause small discrepancies. The formula produces an unrounded mathematical result, while a loan payment is normally stated to cents. This calculator rounds the regular payment before estimating total interest, so its total is consistent with the displayed payment. A lender’s exact schedule may differ by a small amount, especially in the final installment.

The standard formula describes a fully amortizing loan with a fixed rate, equal monthly payments, and no extra payments. It does not model variable rates, skipped or late payments, payment-date conventions, fees added to the balance, or irregular installments. An APR may account for some borrowing costs in a lender’s disclosure, but this calculator uses the APR only as the rate input and does not separately calculate fee effects.

Frequently Asked Questions

What is the monthly amortization formula for a personal loan?
The payment formula is P × r / [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly decimal interest rate, and n is the number of monthly payments.

How do I convert APR to a monthly rate?
For APR entered as a percentage per year, divide it by 1200. For example, 8% APR becomes 0.0066667 per month in decimal form.

Does a personal loan payment include fees?
This formula calculates principal and interest only. Fees or other charges are not added unless they are explicitly represented in the inputs or modeled separately.

Why does the interest portion change each month?
Interest is calculated on the outstanding balance. As principal is repaid, the balance generally falls, so less interest accrues in later periods under a fixed-rate schedule.

Why might a lender’s payment differ from this calculator?
The loan may use different payment dates, a different rate basis, financed fees, or a final-payment adjustment. Use the lender’s disclosed schedule for contract-specific figures.

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

Related

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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