Compound Interest on a Loan: How to Calculate It

This calculator estimates the total interest on a fixed-rate loan repaid with equal monthly payments, using your loan amount, APR, and term. Enter those figures to see the estimated monthly payment and total interest; the calculation assumes the payment is rounded to cents.

Formula

For an installment loan with a fixed annual percentage rate and equal monthly payments, calculate the payment first, then subtract the original principal from all payments combined.

• Monthly rate, r = APR / 1,200. APR is entered as a percentage per year, so this converts it to a decimal monthly rate.
• Number of payments, n = loan term in years × 12.
• Monthly payment, M = P × r / [1 − (1 + r)⁻ⁿ].
• Total interest, I = M × n − P.

P is the amount borrowed in dollars, M is the monthly payment in dollars, and I is the estimated total interest in dollars. The calculator displays the payment to the nearest cent, then uses that displayed payment to calculate total interest. It does not calculate the interest charge on a loan that compounds without regular payments; it models a standard, fully amortizing loan with monthly payments.

Worked Example

Using the calculator’s default figures: P = $20,000, APR = 8%, and a five-year term.

1. Convert the APR to a monthly decimal rate: r = 8 / 1,200 = 0.0066667, or about 0.6667% per month.
2. Find the number of payments: n = 5 × 12 = 60.
3. Apply the payment formula: M = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰] ≈ $405.53 per month, rounded to cents.
4. Multiply the rounded payment by the number of payments: $405.53 × 60 = $24,331.80.
5. Subtract the amount borrowed: $24,331.80 − $20,000 = $4,331.80 estimated total interest.

The result represents interest across all 60 scheduled payments under these assumptions. A lender’s actual payment schedule may differ because of payment dates, rounding, fees, or other contract terms.

Assumptions

• The interest rate stays fixed for the full loan term.
• There are 12 equal payments per year, and payments are made monthly after interest accrues for each period.
• Interest compounds monthly at APR / 12. This calculator treats APR as the nominal annual rate used in the payment formula.
• The loan is fully repaid through the scheduled payments, with the final payment assumed to follow the same rounded amount.
• Fees, taxes, insurance, PMI, and escrow are not included.

Step-by-Step

1. Find the principal. Enter the amount you plan to borrow, not the total amount of all payments. If the loan includes a financed fee, confirm whether that fee is part of the amount on which interest accrues and use the lender’s stated principal.
2. Use the APR specified for the loan. Enter the annual percentage rate as a percentage, such as 8 for 8%, not 0.08. The calculator converts it to a monthly decimal rate by dividing by 1,200. If your loan has a variable rate, a single fixed-rate result cannot show future changes.
3. Enter the term in years. The calculator converts years to monthly payments by multiplying by 12. If the lender quotes a term in months, divide the number of months by 12 before entering it. For a term that does not convert neatly, check that the calculator’s input precision represents the actual number of scheduled payments.
4. Calculate the monthly payment. The payment formula spreads repayment of principal and interest over the term. Early payments generally include a larger interest portion; later payments apply more toward principal, while the total payment stays level in this model.
5. Calculate total interest. Multiply the cent-rounded monthly payment by the number of payments and subtract the original principal. This isolates the estimated interest paid over the full schedule.
6. Compare the estimate with the lender’s figures. Check the stated principal, APR, payment frequency, number of payments, and payment amount. Use the loan disclosure or amortization schedule for a contract-specific total.

Common Mistakes

• Mixing up APR and a monthly rate: Enter the annual percentage as 8 for 8%. Do not enter 0.08 or divide it by 12 yourself; the calculator performs the conversion.
• Using the repayment total as the loan amount: Principal is what is borrowed. Total payments include principal and interest, so entering that total as principal overstates the estimate.
• Assuming every loan uses this payment structure: Interest-only loans, balloon loans, daily-interest calculations, and loans with irregular payments need different methods.
• Rounding too early: Keep precision through the formula and round the payment to cents as shown. Manually rounding the monthly rate or intermediate values can shift the final total.
• Ignoring additional costs or rate changes: Fees and changing rates can affect what is paid. This calculator does not add costs that are not included in its inputs.

Tips

• Use the exact principal, APR, and payment term provided by the lender rather than an approximate rate or term.
• Ask for the payment schedule if you need to see how much of each payment goes to interest and principal. The total-interest figure alone does not show the timing of those portions.
• For a comparison between different loan terms, calculate each term separately using the same principal and rate, and note that the payment and total interest may both change.
• If you plan to make extra payments, this standard calculation does not account for them. A payoff calculator that accepts extra payments is needed to estimate their effect.
• Use the result as an arithmetic estimate, not as a substitute for the lender’s contract figures.

Troubleshooting

If your result differs from a lender’s estimate, first confirm that both calculations use the same principal, APR, number of monthly payments, and payment timing. Check whether the lender’s displayed APR includes costs that are not part of the interest rate used for its payment schedule. Also compare the exact payment: even a small difference, when multiplied across many months, changes total interest.

If the loan has a variable rate, a different compounding or payment frequency, fees added to the balance, a deferred-payment period, or a final payment that differs from the others, this calculator’s assumptions do not match it. Use the lender’s amortization schedule or a calculator designed for those terms. If the entered term cannot represent the lender’s exact payment count, convert the actual count carefully or use a tool that accepts months directly.

Frequently Asked Questions

Is compound interest the same as total interest on a loan?
Not exactly. Compound interest describes interest calculated on a balance that includes previously accrued interest. This calculator estimates total interest for a regularly paid, amortizing loan, where each payment reduces the balance.

Why does the balance change the amount of interest in each payment?
Interest is calculated on the outstanding balance. As payments reduce principal, the amount of interest accruing each month generally falls, assuming the rate remains fixed.

Can I use this for a credit card or an interest-only loan?
Not reliably. Those products may use daily balances, variable rates, minimum payments, or different repayment rules. Their interest and payoff calculations require those details.

Why is my calculated total slightly different from the lender’s total?
Differences can result from payment dates, daily accrual, rounding rules, fees, or an exact payment count that differs from the entered term. Check the lender’s schedule and assumptions.

Does the total include fees or insurance?
No. The calculator uses principal, APR, and term only. Costs not represented by those inputs are excluded.

Can I use the result to estimate savings from extra payments?
No. Extra payments can change the balance and payoff date, but they are not included here. Use a calculation that models the amount and timing of extra payments.

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

Related

• Compound Interest Calculator for Loan Repayment
• Compound Interest for Mortgages: How It Works
• Compound Interest Auto Loan Calculator Explained

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