Calculate Compound Interest on a Loan

This calculator estimates a fixed monthly loan payment and the total interest paid over the loan term using a monthly-rate, level-payment formula. Enter the loan amount, annual percentage rate (APR), and term in years; the results show the monthly payment and total interest, not the balance that would result from leaving interest unpaid to compound.

Formula

For a loan repaid in equal monthly installments, the calculator uses the standard amortizing-payment formula. The payment is M = P × r ÷ [1 − (1 + r)⁻ⁿ], where r = APR ÷ 1200 and n = 12 × y. Total interest is I = M × n − P, using the monthly payment rounded to cents.

• P is the starting loan principal, in dollars.
• APR is the entered annual percentage rate, as a percentage number; for example, enter 8 for 8%.
• r is the monthly interest rate as a decimal.
• y is the term in years, and n is the number of monthly payments.
• M is the monthly payment in dollars; I is total interest in dollars.

The payment equation spreads principal and interest across the scheduled payments so that, under its assumptions, the balance reaches zero after the final payment. In the calculator, the payment formula is displayed without an internal rounding function, while the result is displayed to two decimal places. The total-interest output uses the displayed, cent-rounded payment.

Worked Example

Using the defaults—$20,000 principal, 8% APR, and a five-year term—there are 5 × 12 = 60 payments. The monthly rate is 8 ÷ 1200 = 0.0066667.

1. Substitute into the payment formula: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. Calculate the monthly payment: approximately $405.53 when rounded to cents.
3. Calculate total paid using the rounded payment: $405.53 × 60 = $24,331.80.
4. Subtract the original principal: $24,331.80 − $20,000 = $4,331.80 total interest.

The headline result is the monthly payment, $405.53. Small differences can arise if intermediate values are rounded differently; the calculator applies its displayed formula and rounds output to cents.

Assumptions

• The APR is fixed throughout the term and is treated as a nominal annual rate divided by 12.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest accrues monthly at APR ÷ 12 on the outstanding balance.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and any separately financed charges.

What Compound Interest Means on a Loan

Compound interest means interest can be calculated on a balance that already includes previously accrued interest. But a conventional amortizing loan with regular payments is not calculated simply by adding interest to the original principal and leaving it there. Each period, interest is generally calculated on the remaining balance; the payment covers that period’s interest and reduces principal by the rest.

For example, at the start of the default loan, one month’s interest is approximately $20,000 × 0.0066667 = $133.33. Of the $405.53 payment, about $272.20 then reduces principal. Later, because the balance is lower, the interest portion falls and more of the scheduled payment goes toward principal. This changing split is amortization.

Therefore, “compound interest on a loan” can refer to different calculations. This calculator estimates the cost of a fully amortizing loan with monthly payments. It does not calculate the future value of unpaid debt under capitalization, a balloon balance, or a loan whose interest is added to principal without regular payments.

How to Use and Read the Results

Enter the principal actually borrowed, the APR supplied for the loan, and the scheduled term. APR is entered as a percentage, not a decimal: type 8 for 8%, rather than 0.08. The term is in years, so a three-year term is entered as 3. The result estimates a monthly payment and the interest across all scheduled payments.

Total interest is not the total amount repaid. To get total scheduled payments, add principal to interest; in the example, $20,000 + $4,331.80 = $24,331.80. Nor does the interest figure represent the entire cost of borrowing when fees or other charges apply. If a lender provides a payment quote or disclosure, use its exact terms when comparing the figure with the estimate.

Common Calculation Problems and Limits

• Mixing up APR and monthly rate: the formula converts an annual percentage to a monthly decimal by dividing by 1,200. Do not divide by 12 and then treat the percentage as a decimal without converting it.
• Assuming every loan compounds this way: payment frequency, rate structure, payment dates, and capitalization rules can differ. The calculator models monthly payments at a fixed rate.
• Rounding at the wrong stage: monthly payments are normally made in cents, so multiplying an unrounded payment by the number of months may not match a total based on cents-rounded installments.
• Including charges that are not entered: fees, optional products, taxes, insurance, and escrow can change the amount due or total cost. This calculator has no inputs for them.
• Assuming early payoff or extra payments are included: the estimate follows the original schedule. Extra payments, missed payments, a variable APR, and a final adjusted payment are not modeled.

At a zero interest rate, the payment would simply be principal divided by the number of installments, but this calculator’s rate input begins at 0.01% because its formula divides by the monthly rate. Actual loan terms may also define APR, accrual, and payment timing differently; enter the lender’s quoted figures and treat the output as an estimate.

Frequently Asked Questions

How do you calculate compound interest on a loan?
For a fixed-rate loan with equal monthly payments, first calculate the payment using the amortizing formula: M = P × r ÷ [1 − (1 + r)⁻ⁿ]. Then estimate total interest as the rounded monthly payment multiplied by the number of payments, minus the principal.

Is loan interest compounded monthly?
This calculator assumes monthly accrual at APR ÷ 12. A particular loan’s contract may use a different accrual convention or payment schedule, so check the lender’s disclosures for the applicable method.

Why does the interest part of my payment decrease?
With a level-payment amortizing loan, interest for each period is based on the remaining principal. As payments reduce that balance, the interest charge generally decreases and a larger portion of the same payment repays principal.

Does this calculator include extra payments or fees?
No. It assumes the scheduled fixed monthly payment and excludes extra payments, fees, taxes, insurance, PMI, and escrow. Those items require separate figures and can change total cost.

Is APR the same as the monthly interest rate?
No. APR is entered as an annual percentage. Under this calculator’s assumption, the monthly decimal rate is APR divided by 1,200; an 8% APR corresponds to about 0.006667 per month.

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

Related

• Loan Refinance Rules: What Changes and What to Check
• Loan Refinance Rates: Estimate Payments and Interest
• Loan Refinance Rate Comparison Calculator

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