Compound Interest on a Loan: Formula and Calculator

This calculator estimates the total interest on a loan that compounds monthly, using the starting balance, annual percentage rate (APR), and loan term. Enter those figures to see the projected monthly payment and total interest; the calculation assumes equal monthly payments and a fixed rate.

Formula

For a standard loan with equal monthly payments, first calculate the monthly interest rate and number of payments. Then use the level-payment formula to find the payment. The calculator rounds that payment to cents and uses the rounded amount to estimate total interest.

Monthly rate: r = APR / 1200
Number of payments: n = years × 12
Monthly payment: M = P × r / [1 − (1 + r)⁻ⁿ]
Total interest: I = M × n − P

• P is the original loan principal, in dollars.
• APR is the annual percentage rate entered as a percentage, such as 8 for 8% per year.
• r is the monthly interest rate as a decimal.
• n is the number of monthly payments.
• M is the monthly payment, in dollars, rounded to the nearest cent.
• I is the estimated total interest paid, in dollars.

Compound interest means interest is calculated on the outstanding balance, which includes any unpaid interest. On an ordinary amortizing loan, each regular payment covers interest accrued for the period and reduces principal by whatever remains. The balance therefore changes over time. The formula assumes monthly periods and a payment at the end of each period.

Worked Example

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

1. Convert the annual APR to a monthly decimal rate: r = 8 / 1200 = 0.0066667, or about 0.66667% per month.
2. Calculate the number of monthly payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: M = 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. Calculate total interest using the rounded payment: I = $405.53 × 60 − $20,000 = $4,331.80.

The total of the 60 rounded payments is $24,331.80, including the $20,000 principal and $4,331.80 estimated interest. Actual statements may differ slightly because of payment dates, daily interest calculations, rounding, or fees.

Assumptions

• The APR is fixed for the full loan term.
• Payments are equal, made monthly at the end of each period, and begin after one monthly interest period.
• Interest compounds monthly at APR / 12.
• Fees, taxes, insurance, PMI, and escrow are not included. The calculation does not model a changing balance from extra, missed, or late payments.

What You’ll Need

• The amount borrowed, not the total amount you expect to repay.
• The loan’s APR and term from the lender’s loan documents or disclosure. If the rate can change, this fixed-rate estimate will not represent later rate changes.
• A calculator or the calculator fields above. Use consistent units: enter APR as a percentage and term in years.

Step-by-Step

1. Find the principal. Enter the amount financed as the loan amount. If some charges are added to the balance, use the financed amount shown in the loan documents rather than the amount you receive in cash.
2. Enter the APR. Use the annual percentage rate as a number: enter 8 for 8%, not 0.08. The calculator divides by 1,200 to convert an annual percentage into a monthly decimal rate.
3. Enter the term. Put the repayment period in years. For example, a 30-month term is 2.5 years. For an exact term that is not a whole number of months, confirm the payment schedule with the lender; this model converts years to months.
4. Calculate the monthly payment. The payment formula finds the fixed amount that pays interest and gradually repays principal over the selected number of monthly periods. It assumes every payment arrives on schedule.
5. Calculate total interest. Multiply the displayed, cent-rounded monthly payment by the number of payments, then subtract the original principal. This estimates total interest across the full term, not interest for one month.
6. Check the result against the disclosure. Compare the inputs and payment schedule with the lender’s documents. Look for payment frequency, fees added to the balance, a variable rate, a final balloon payment, or other terms the simple formula does not model.

Common Mistakes

• Entering APR as a decimal: For 8%, type 8. The formula performs the percentage conversion itself.
• Using the whole term as the number of periods: Monthly payments require months, so a five-year term means 60 payments.
• Confusing interest with total repayment: Total repayment includes principal; total interest is the amount above principal.
• Assuming all loans compound monthly: Some agreements calculate interest daily or use different payment timing. The calculator’s monthly assumption may then produce a different estimate.
• Ignoring fees or payment changes: Fees, late payments, extra payments, and variable rates can alter the balance and total cost.
• Rounding too early: Keep full precision while converting the rate and applying the formula; round the payment to cents as shown, then use that rounded payment in the total.

Tips

Use figures from the same loan offer and verify whether the quoted APR includes costs that are financed into the principal. If comparing estimates, keep the principal, rate, term, payment timing, and fee treatment consistent. You can also calculate interest manually: for each month, multiply the opening balance by the monthly rate to estimate interest, subtract that interest from the payment to find principal repaid, then subtract principal repaid from the balance. Repeat for each payment; rounding and exact payment dates can create small differences.

For an interest-only period, a balloon payment, biweekly payments, daily compounding, or a changing rate, this level-payment formula is not enough. Use the schedule specified by the lender or a calculator that models those details. A lower payment caused by a longer term does not mean lower total interest; check both outputs and the complete repayment schedule without treating this estimate as a recommendation.

Troubleshooting

• The result differs from a lender quote: Check whether the quote uses a different financed principal, exact payment dates, daily accrual, fees, or rounding. Confirm the term is the number of scheduled monthly payments.
• The payment seems too low or high: Recheck APR units and the principal. A percentage entered as 0.08 instead of 8 makes the modeled rate much smaller; entering 8 as 8% is correct.
• The balance does not reach zero in your own schedule: Use the actual payment amount and dates, and account for the final payment being adjusted. Small residual balances can result from rounding.
• The loan has a variable rate or unusual payment structure: Do not rely on one fixed-rate result for the full term. Ask the lender for the applicable schedule and recalculate each period only if you have the required rate and payment details.

Frequently Asked Questions

How do I work out compound interest on a loan?
For a fixed-rate loan with equal monthly payments, calculate the monthly rate as APR / 1200, find the payment with the amortizing-loan formula, then multiply the rounded payment by the number of payments and subtract the principal.

Is compound interest the same as APR?
No. APR is an annual rate expressed as a percentage. Compounding describes how interest accrues over time. The calculator uses APR / 12 as the monthly rate and does not separately model additional fees.

Does every loan compound monthly?
No. Some loans accrue interest daily or use another method. Check the loan documents for the interest calculation and payment schedule before relying on a monthly estimate.

Why can my lender’s total differ from this result?
The lender may use exact payment dates, daily interest, fees, a different balance, or a final adjusted payment. The calculator also assumes the rate and scheduled payment stay fixed.

Do extra payments reduce total interest?
They can reduce the outstanding principal sooner, which can lower later interest, but this calculator does not include extra payments. Check how additional payments are applied and request an updated amortization schedule.

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