Compound Interest Loan Calculation: Formula and Example

A compound interest loan calculation estimates the monthly payment and total interest when interest is added to the balance over time. Enter the amount borrowed, annual interest rate, and term to see the payment and total interest under a fixed-rate, monthly-payment model.

Formula

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

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

Here, P is the original loan principal in dollars, r is the monthly interest rate expressed as a decimal, and n is the number of monthly payments. With an APR entered as a percentage per year, this calculator uses r = APR ÷ 1200 and n = years × 12. It rounds the monthly payment to the nearest cent, then calculates total interest as rounded payment × number of payments − principal.

Although the expression is sometimes described as a compound-interest formula, it is specifically the level-payment amortization formula. Each month, interest is calculated on the current unpaid balance; the payment covers that interest and reduces principal by what remains. The balance therefore changes after every payment.

Worked Example

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

1. Convert APR to a monthly decimal rate: 8 ÷ 1200 = 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].
4. The unrounded payment is about $405.53; rounded to cents, the monthly payment is $405.53.
5. Total of the rounded payments: $405.53 × 60 = $24,331.80.
6. Subtract the original principal: $24,331.80 − $20,000 = $4,331.80 in total interest.

The interest portion is not the same in every payment. At the start, the balance is larger, so more of a payment goes to interest. As principal falls, the interest charged each month generally falls too, leaving more of the same scheduled payment to reduce principal.

Assumptions

• The interest rate stays fixed for the entire term.
• Payments are equal, made monthly, and treated as payments at the end of each monthly period.
• Interest compounds monthly at APR divided by 12.
• The calculation excludes fees, taxes, insurance, PMI, and escrow because they are not calculator inputs.

How the Calculation Works

At each payment date, the balance has accrued a month of interest at the monthly rate. The payment first accounts for that interest; the remainder reduces the amount owed. The formula chooses a payment that, under its assumptions, brings the balance to zero after the specified number of payments.

For instance, at the first month in the example, interest is approximately $20,000 × 0.0066667, or $133.33. Of the $405.53 payment, about $272.20 therefore goes toward principal. The following month’s interest is based on the lower balance, not the original $20,000. Small differences can arise in an actual schedule because lenders may calculate daily interest, use different rounding conventions, or set payment dates that do not align with monthly periods.

The calculator reports total interest as the sum of the rounded scheduled payments minus the original principal. It does not mean that the full payment is interest: part of each payment repays borrowed principal. It also does not include costs that may be charged separately or added to the amount financed.

Compound Interest Versus Simple Interest

With simple interest, interest is calculated only on the original principal for the relevant period. Compound interest means unpaid interest can itself become part of the balance on which later interest is calculated. An amortizing loan has a changing balance because regular payments reduce principal; it is not accurately represented by simply multiplying the original amount by the APR and the number of years.

Some loans use a different structure, including interest-only payments, irregular payment schedules, variable rates, or a balance that grows when payments do not cover accrued interest. This calculator does not model those arrangements. The word “compound” alone does not determine a loan’s payment method: the contract’s rate convention, payment schedule, and balance rules matter.

When to Use This Estimate

Use this calculation to understand how principal, rate, and duration relate in a conventional fixed-rate loan with equal monthly payments. It can help you check the arithmetic in a quoted payment or see how a different input changes the mathematical estimate. The entered APR and term should come from the relevant lender disclosure or loan documents; the default values are only an example, not a statement about available rates.

• Enter the amount actually financed as the principal. If an eligible cost is rolled into the loan, include it only if it is part of that financed amount.
• Enter the annual APR as a percentage, such as 8 for 8%, not 0.08.
• Enter the term in years. The formula converts years to monthly payments.
• Read the payment and total interest as estimates for the stated assumptions, not as a complete accounting of every loan cost.

Common Calculation Mistakes and Limits

A frequent error is using APR as the monthly rate without dividing by 12, or entering 8% as 0.08 in a field that expects 8. The calculator converts a percentage APR to a monthly decimal by dividing by 1200. Another error is treating all payments as interest or assuming that multiplying principal by APR and years gives the total interest on an amortizing loan.

Rounding also matters. The calculator rounds the scheduled payment to cents before multiplying by the number of payments, so its total reflects repeated payments at that rounded amount. A lender’s final payment or disclosed total may differ slightly because of rounding, payment timing, daily accrual, fees, or other contract details. A variable rate can change payments or the payoff timeline, so a single fixed APR cannot represent its future cost. The formula also presumes the scheduled payments are made as modeled; extra payments, missed payments, late charges, and early payoff are not included.

Frequently Asked Questions

How do I calculate compound interest on a loan?
For a standard fixed-rate loan with equal monthly payments, convert APR to a monthly rate, use the amortization payment formula, then multiply the rounded payment by the number of months and subtract principal to estimate total interest.

Is compound interest calculated on the original loan amount?
In an amortizing loan, monthly interest is generally calculated on the outstanding balance under the loan’s stated method. Payments reduce that balance over time, so later interest charges can differ from earlier ones.

Why is my lender’s payment different from this result?
The lender may use different payment dates, daily interest accrual, rounding, fees, or a different rate or balance structure. Compare the calculator inputs with the lender’s disclosed terms and calculation method.

Does this include fees or insurance?
No. The estimate covers principal and modeled interest only. It excludes fees, taxes, insurance, PMI, and escrow unless those costs are incorporated into the principal you enter.

Can I use this for a variable-rate or interest-only loan?
Not as a complete estimate. The calculation assumes a fixed rate and level monthly payments that repay principal over the stated term; variable-rate and interest-only structures require different inputs or methods.

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