Personal Loan Amortization Calculator Formula

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

Formula

For a loan repaid in equal monthly payments, the payment formula is:

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.
• n is the number of monthly payments. For a term in years, n = years × 12.

The calculator rounds the monthly payment to cents. Its total-interest estimate is payment × n − P, using that rounded payment. APR is divided by 12 to produce a monthly rate under the calculator’s monthly-rate assumption; it is not entered as a decimal such as 0.08. The input 8 means 8% APR.

Worked Example

Using the calculator’s default inputs: P = $20,000, APR = 8%, and term = 5 years.

1. Convert the APR to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066666667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the formula: payment = 20,000 × 0.0066666667 ÷ [1 − (1 + 0.0066666667)⁻⁶⁰].
4. The monthly payment is approximately $405.53 after rounding to cents.
5. Total of scheduled payments = $405.53 × 60 = $24,331.80. Estimated total interest = $24,331.80 − $20,000 = $4,331.80.

Calculations use unrounded values internally for the payment and round the displayed result to cents. The total-interest result then uses the displayed, cent-rounded payment, so it follows the calculator’s stated method.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and occur at the end of each monthly period.
• Interest accrues monthly at APR divided by 12.
• Fees, taxes, insurance, and other charges are not included; the calculator has no inputs for them.

How Amortization Works

Amortization is the process of paying down a loan through scheduled payments. Each payment covers interest accrued for the period and reduces the outstanding principal by the remainder. Early in a level-payment schedule, the balance is larger, so more of the payment generally goes toward interest. As the balance falls, the interest portion falls and more of each payment reduces principal.

For a monthly schedule, a simple way to calculate one period is to multiply the balance at the start of that period by the monthly rate to estimate its interest. Subtract that interest from the payment to find the principal reduction, then subtract the reduction from the starting balance. Repeating the calculation month by month produces an amortization schedule. Minor differences can arise when a lender’s actual daily-interest method, payment dates, or rounding conventions differ from this monthly model.

When to Use the Estimate

Use the formula to understand the relationship between principal, APR, and term, or to check a lender’s quoted scheduled payment against the same assumptions. It is a mathematical estimate, not a full loan quote. Enter the amount actually financed and the APR and term shown in the lender’s disclosure; ask the lender how any financed charges affect those figures.

The outputs answer two different questions:

• Monthly payment estimates the regular scheduled payment for principal and interest.
• Total interest estimates the interest paid across all scheduled payments, given the rounded payment and full term.

Total payments are not the same as total interest: total payments include repayment of the original principal. The calculator also does not show the date-specific payoff amount, which may reflect accrued interest or other amounts not represented in this fixed monthly schedule.

Common Mistakes and Limits

• Entering the wrong APR units: Enter 8 for 8%, not 0.08 or 8.0 as a decimal fraction. The formula converts the percentage to a monthly decimal rate.
• Mixing years and months: This calculator accepts a term in years and multiplies it by 12. If working by hand with months, use the total number of monthly payments directly.
• Expecting a zero-interest result: The standard formula divides by the monthly rate, so the rate input starts at 0.01% rather than zero. A zero-interest loan has a different simple calculation: principal divided by the number of payments.
• Ignoring rounding: The payment is rounded to cents, and total interest uses that displayed payment. A lender may round each period differently, so a small discrepancy is possible.
• Assuming extra payments are included: Additional principal payments, late payments, skipped payments, variable rates, and changing payment dates are not modelled. They can change the payoff timing and interest total.

The formula assumes a standard level-payment loan with periodic monthly compounding. It does not account for fees or other charges, nor does it determine eligibility, approval, or a lender’s actual terms. Use the lender’s stated figures when comparing the calculator’s estimate with a disclosure.

Frequently Asked Questions

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

How do I convert APR to a monthly interest rate?
When APR is entered as a percentage, divide it by 1200. For example, 8% APR gives a monthly rate of 8 ÷ 1200, or about 0.006667 as a decimal.

Does a longer loan term reduce total interest?
Not necessarily. For the same principal and rate, a longer term usually produces a lower scheduled payment but more payment periods, which can increase the total interest calculated over the full schedule.

Does this calculator include loan fees?
No. It calculates principal-and-interest payments from the entered amount, APR, and term. Fees and other charges are excluded unless they are already reflected in the loan amount or APR you enter.

Why might my lender’s payment differ?
The lender may use different rounding, payment dates, daily interest, financed fees, or other contract terms. Compare the same principal, APR, term, and payment assumptions, and refer to the lender’s disclosure for the exact figures.

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

Related

• Loan Amortization Excel: Formula and Schedule
• Loan Amortization Excel With Extra Payments
• Loan Amortization: Definition, Formula and Example

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