Compound Interest Formula for a Loan: Calculator

This compound-interest loan calculator estimates the monthly payment and total interest for a fixed-rate loan with monthly payments. Enter the amount borrowed, annual percentage rate (APR), and term in years; the results use a standard level-payment formula and are estimates, not a lender’s payoff quote.

Formula

For a loan repaid through equal monthly payments, the payment is calculated with the amortizing-loan formula:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal. With an annual APR entered as a percentage, r = APR ÷ 1200.
• n is the number of monthly payments: loan term in years × 12.
• Payment is the monthly payment in dollars, rounded to the nearest cent.

Total interest is calculated as monthly payment × number of payments − amount borrowed. The calculator uses the rounded monthly payment for that total. The payment formula is the standard fixed-rate amortization formula; it is not the simple compound-growth formula A = P(1 + r)ⁿ, which describes a balance left to grow without regular repayments.

Worked Example

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

1. Convert the annual percentage rate to a monthly decimal rate: r = 8 ÷ 1200 = 0.0066667.
2. Find the number of monthly payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = approximately $405.53 per month after rounding to cents.
4. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The calculator therefore displays a monthly payment of $405.53 and total interest of $4,331.80. Calculations performed with rounded intermediate values can differ slightly from calculations that retain more precision until the final step.

Assumptions

• The interest rate is fixed throughout the entered term.
• Payments are equal, made monthly, and occur at the end of each monthly period.
• Interest accrues monthly using APR divided by 12; this is the calculator’s compounding convention.
• The estimate excludes fees, taxes, insurance, PMI, and escrow because there are no inputs for them.

What Compound Interest Means for a Loan

Interest is the cost charged for borrowing money. When interest is calculated on a balance that includes previously unpaid interest, it is commonly described as compounding. A regular loan payment changes the balance, so interest in a given month is generally calculated on the outstanding principal rather than on the original loan amount forever.

In a typical amortizing schedule, each payment covers the interest accrued for that period and reduces principal by the remainder. Early in repayment, the balance is larger, so the interest portion is often larger. As principal falls, the interest portion tends to shrink and more of each level payment goes toward principal. The exact schedule depends on the contract’s rate, timing, and payment rules.

“Compound interest formula for a loan” can refer to more than one calculation. If no payments are made and interest compounds at a periodic rate, the growth formula is A = P(1 + r)ⁿ. For an installment loan with equal payments, the payment formula above is the relevant one because it accounts for the balance being reduced over time. Applying the no-payment growth formula to a regularly repaid loan would not calculate its scheduled payment.

How to Use and Interpret the Calculator

Enter the principal actually borrowed, the APR as a percentage per year, and the full term in years. For example, type 8 for an 8% APR, not 0.08. The calculator converts that input to a monthly decimal rate and converts years to months. Its output is a mathematical estimate under the stated assumptions, not a complete monthly housing or borrowing cost.

The monthly payment is the level amount needed to amortize the entered balance over the stated number of monthly periods under the formula. Total interest is the sum of those rounded payments less the original principal. Total payments can be found by adding the principal to total interest; they do not include charges omitted from the calculation.

• Use the loan amount, APR, and term stated in the lender’s current disclosure or offer. Do not assume an advertised rate applies to a particular borrower.
• Check whether the APR and payment schedule match the calculator’s monthly assumptions.
• Compare the estimate with the lender’s disclosed payment schedule and ask how any additional charges are treated.

Common Limits and Mistakes

A common error is confusing an APR expressed as a percentage with a decimal rate: the calculator requires 8 for 8%, then divides by 1200 internally. Another is entering months in the years field. A 60-month term should be entered as 5 years. Rounding also matters: this calculator rounds each scheduled payment to cents and uses that rounded amount for total interest, while a lender’s final payment may be adjusted to clear a remaining balance.

The estimate may not match a loan with a variable rate, irregular payment dates, interest-only periods, deferred payments, a balloon payment, or a different compounding convention. Fees may be financed into the balance or charged separately, and the calculator does not model either treatment. A loan with no payment, a payment schedule that changes, or a payoff before the full term needs a different calculation.

For a precise schedule, use the lender’s disclosed principal, rate, payment dates, and fee treatment. If an amount differs, check whether it reflects rounding, a first payment period of unusual length, an added charge, or a rate convention not represented here.

Frequently Asked Questions

What is the compound interest formula for a loan payment?
For equal monthly payments, use Payment = P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly rate as a decimal, and n is the number of payments.

Is loan interest compounded monthly?
This calculator assumes monthly accrual at APR divided by 12. A particular loan’s contract and disclosure determine its actual rate and interest calculation method.

Is APR the same as the monthly interest rate?
No. APR is entered here as a yearly percentage. The formula converts it to a monthly decimal by dividing the percentage number by 1200.

Why does the interest portion change when my payment stays the same?
Interest is calculated on the outstanding balance. As regular payments reduce principal, less interest accrues in later periods, so a larger share of the same payment can reduce principal.

Does total interest include fees or insurance?
No. This calculator subtracts the original principal from the sum of rounded monthly payments. It does not include fees, taxes, insurance, PMI, or escrow.

Why might my lender’s payment differ from this estimate?
The lender may use different payment dates, rounding, rate conventions, financed fees, or other contract terms. The result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Refinance a 401(k) Loan? Costs and Key Rules
• Refinance a Personal Loan After Bankruptcy?
• Personal Loan Refinance Calculator: Payment and Interest

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