Personal Loan Calculator Monthly Repayment Formula

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

Formula

For a fixed-rate loan with equal monthly payments, the standard payment formula is:

Monthly payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100, or APR ÷ 1,200 when APR is entered as a percentage.
• n is the total number of monthly payments: loan term in years × 12.

The calculator rounds the monthly payment to the nearest cent. Its total-interest output is the rounded monthly payment multiplied by the number of months, minus the original loan amount. This reflects the fact that actual scheduled payments are made in cents. A lender’s final payment may differ slightly because of its payment dates, rounding method, or other contract details.

Worked Example

Using the calculator’s default inputs—$20,000 borrowed, 8% APR, and a 5-year term—first convert the APR and term:

1. Monthly rate: 8 ÷ 1,200 = 0.0066667.
2. Number of payments: 5 × 12 = 60.
3. Substitute: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
4. The unrounded payment is about $405.53; rounded to cents, the monthly payment is $405.53.
5. Estimated total paid: $405.53 × 60 = $24,331.80. Estimated total interest: $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The APR is fixed for the full term, and the loan is repaid in equal monthly installments.
• Payments are assumed to occur monthly, with interest accruing monthly at APR divided by 12.
• The calculation does not include fees, taxes, insurance, or other charges unless they are included in the loan amount or represented by an input. It does not model a changing rate or irregular payment schedule.

How Monthly Repayments Work

A level payment contains both interest and principal. In the early part of a fully amortizing loan, the outstanding balance is larger, so more of each payment goes toward interest. As the balance falls, the interest portion generally shrinks and more of the same payment reduces principal. If payments are made as scheduled under the assumptions, the balance reaches zero after the final installment.

For example, in the first month of the worked example, approximate interest is $20,000 × 0.0066667, or $133.33. Of the $405.53 payment, roughly $272.20 therefore reduces principal. The next month’s interest is calculated on the lower balance. This is why multiplying the original loan amount by the monthly rate alone does not give the full repayment: that result is only the first month’s approximate interest, not the combined principal-and-interest payment.

How to Use and Read the Estimate

Use the amount and term shown in the lender’s offer, and enter the APR as a percentage per year—not as a decimal or a monthly rate. For an offer showing an 8% APR, enter 8, not 0.08 or 0.00667. If a lender provides a separate fee or financed charge, check whether it is already included in the amount being borrowed before entering a figure. Ask the lender for the exact APR and payment schedule if those details are unclear.

The monthly-payment result is an estimate of the recurring installment under the stated assumptions. The total-interest figure estimates how much interest is paid over the full term when each installment is the calculator’s rounded amount. It is not the total cost if the contract adds charges that are outside the formula. Changing the input term or APR changes the result; the calculator does not determine what a lender will offer or whether an application will be approved.

Common Formula Mistakes and Limits

• Mixing rate units: The formula needs a monthly decimal rate. For an APR entered in percent, divide by 1,200. Dividing by 12 without also converting percent to decimal makes the rate 100 times too large.
• Using years as months: Convert a term in years to total payments by multiplying by 12. A five-year term means 60 monthly payments, not five.
• Confusing APR with the interest rate: APR is an annualized borrowing-cost measure whose treatment may reflect certain charges, depending on how it is disclosed. This calculator uses the entered APR as a fixed monthly rate divided by 12; it does not separately model fees or reproduce every lender’s disclosure calculation.
• Rounding too early: Keep the rate and formula unrounded through the calculation, then round the payment to cents. Rounding intermediate values can shift the result by a few cents.
• Assuming every loan is level-payment: The formula does not represent variable rates, interest-only periods, skipped or irregular payments, extra payments, or a final payment adjusted by a lender.

If a quoted payment differs from this estimate, compare the amount financed, APR, term, timing, and any charges included in the contract. Differences do not automatically mean either calculation is wrong; the assumptions may not match.

Frequently Asked Questions

How do I calculate a personal loan payment by hand?
Convert APR to a monthly decimal by dividing by 1,200, multiply the years by 12 to get the payment count, and substitute those values with the loan amount in the formula above.

Does a longer loan term lower the monthly payment?
With the same principal and fixed rate, spreading repayment over more months generally lowers each scheduled payment, but it also means interest accrues over a longer period. The calculator estimates the effect for the figures entered.

Is the monthly payment the same as monthly interest?
No. A scheduled payment typically covers both interest and part of the principal. Monthly interest is calculated on the remaining balance; the payment formula accounts for the changing balance over the term.

Why is my lender’s quoted payment different?
The lender may use a different amount financed, APR, term, payment date, rounding convention, or include charges that this estimate excludes. Compare the assumptions with the lender’s written figures.

Can I use this formula for a variable-rate loan?
It can estimate a payment for a specified rate held constant, but it cannot predict payments after a rate changes. A changing rate can alter the payment, repayment period, or both, depending on the contract.

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

Related

• Debt-to-Income Ratio Calculator (DTI)
• Credit Card Payoff Calculator: Months to Pay Off and Interest
• Personal Loan Calculator With Origination Fee: Payment, Cash and APR

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