Compound Interest Formula for Loan Repayment

This calculator estimates the fixed monthly payment and total interest for a loan repaid in equal monthly installments, using the amount borrowed, annual percentage rate (APR), and term. Enter those three values to see the scheduled payment and the interest implied by the formula.

Formula

For a loan with a fixed periodic interest rate and equal payments made at the end of each period, the payment formula is:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the original principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 12 ÷ 100.
• n is the number of monthly payments: years × 12.
• Payment is the scheduled monthly amount, in dollars.

The calculator’s expression uses APR divided by 1,200 to convert a percentage per year to a monthly decimal rate. Total interest is calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal: Total interest = Payment × n − P. The payment is rounded to cents before the total is calculated.

Worked Example

Using the calculator’s defaults—$20,000 principal, 8% APR, and a five-year term—there are 5 × 12 = 60 monthly payments. The monthly rate is 8 ÷ 1,200 = 0.0066667.

1. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The resulting scheduled payment is approximately $405.53 per month, rounded to the nearest cent.
3. Multiply the displayed payment by the number of payments: $405.53 × 60 = $24,331.80.
4. Subtract the principal: $24,331.80 − $20,000 = $4,331.80 total interest.

Small differences can arise if a separate calculation keeps extra decimal places throughout rather than rounding the payment to cents as this calculator does.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal monthly payments made at the end of each month.
• Interest compounds monthly at APR ÷ 12, with no separate daily-interest adjustment.
• Fees, taxes, insurance, PMI, and escrow are not included; the calculator has no inputs for them.

How Compound Interest Works in Loan Repayment

Compound interest means interest is calculated on a balance that can include previously accumulated interest. In a standard amortizing loan, the scheduled payment is designed to cover the period’s interest and reduce principal over time. Early in repayment, the outstanding balance is relatively high, so more of a payment goes toward interest. As principal falls, the interest portion generally falls too, while the payment stays level under the assumptions above.

This is why a loan’s interest cannot usually be found by simply multiplying the starting principal by the APR and the number of years. That simple-interest calculation ignores the changing balance and the timing of repayments. The payment formula accounts for the fact that each installment reduces the balance, while interest continues to accrue on what remains.

When to Use This Estimate

Use this calculation to understand the mathematical effect of a stated principal, APR, and repayment term on equal monthly installments. It can also help show how the term affects the payment-interest tradeoff: holding the principal and rate constant, a longer term generally spreads repayment over more months and increases the total interest under this model.

Enter the APR and term from the lender’s loan disclosure or other relevant loan information. The default values are illustrative inputs, not a statement about available or typical loan terms. If a lender quotes a payment that differs, check whether the quote includes fees, uses a different rate convention, has irregular payment dates, or rounds interest differently.

Common Mistakes and Limits

• Confusing APR with a monthly rate: The formula needs a monthly decimal rate, so divide the annual percentage by 1,200. For example, 8% becomes 0.0066667 per month, not 0.08.
• Mixing years and months: This calculator takes the term in years and converts it to months. A five-year term means 60 payments, not five.
• Assuming the payment is the full borrowing cost: The displayed total interest excludes fees and other charges. A lender’s total repayment figure may include items this calculator does not model.
• Expecting the same result for every loan: Variable rates, irregular payments, interest-only periods, balloon payments, daily accrual, or payment dates other than month-end can change the result.
• Rounding differently: The calculator rounds the monthly payment to cents, then uses that rounded amount to compute total interest. A lender may handle rounding at each payment or calculate accrual using more detailed dates.

This is a standard fixed-rate amortization estimate, not a universal formula for every arrangement that may be described as compound interest. For a changing rate or non-level payment schedule, the balance and interest must be calculated period by period using the terms that apply.

Frequently Asked Questions

What is the compound interest formula for loan repayment?
The standard level-payment formula is Payment = P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the periodic rate as a decimal, and n is the number of payments.

Is APR divided by 12 or 1,200?
For an APR entered as a percentage, divide by 1,200 to get a monthly decimal rate. Dividing by 12 gives a monthly percentage, which must then be divided by 100 before use in the formula.

Does every loan use compound interest?
No single formula covers every loan. This calculator models fixed-rate, monthly amortization with equal end-of-month payments. Contract terms may use other accrual methods or payment structures.

Why does the interest portion change when the monthly payment stays the same?
Interest for each period is based on the remaining balance. As payments reduce principal, less interest accrues in later periods, leaving more of a level payment to reduce principal.

Does the total interest include fees or insurance?
No. It is the scheduled total of payments minus principal under the stated assumptions. Get any applicable charges and the exact repayment figures from the lender.

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

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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