Compound Interest Calculator for Loan Repayment

A compound interest loan repayment calculator estimates the fixed monthly payment needed to repay a loan, along with total interest, using the amount borrowed, annual percentage rate (APR), and term. Enter those three figures to see the estimated payment and interest cost; this standard calculator assumes monthly payments and a fixed rate.

Formula

The calculator applies the standard fixed-payment amortization formula. It converts the annual APR to a monthly rate, then calculates the equal payment that brings the balance to zero after the selected number of monthly payments:

Monthly payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the starting loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 100 ÷ 12, or APR ÷ 1200 when APR is entered as a percentage.
• n is the number of monthly payments: loan term in years × 12.

Total interest is calculated as the rounded monthly payment multiplied by the number of payments, minus the original principal: total interest = monthly payment × n − P. The displayed payment is rounded to cents before the total interest is computed. In practice, a lender may adjust the final payment or calculate interest under different contract terms.

Worked Example

Using the calculator’s defaults—$20,000 principal, 8% APR, and a 5-year term—the monthly rate is 0.08 ÷ 12 = 0.0066667, and the number of payments is 5 × 12 = 60.

1. Payment = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. The unrounded result is approximately $405.53; rounded to cents, the monthly payment is $405.53.
3. Total of the rounded payments = $405.53 × 60 = $24,331.80.
4. Estimated total interest = $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the full term.
• Payments are equal, made monthly, and assumed to occur at the end of each monthly period.
• Interest compounds monthly using the APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and optional add-ons are not included.

How Compound Interest Applies to Loan Repayment

With a loan, interest is generally charged on the unpaid balance, rather than repeatedly added to the original amount while the borrower makes no payments. Each payment first covers interest accrued for that period; the remainder reduces principal. Because the balance declines, the interest portion of a level payment usually shrinks over time while the principal portion grows.

For example, at the start of the illustrated loan, one month’s interest on $20,000 at a monthly rate of 0.0066667 is about $133.33. Of the $405.53 payment, roughly $272.20 therefore goes toward principal. Later payments allocate more toward principal because interest is calculated on a smaller balance. This is amortization: the balance is gradually repaid through scheduled payments.

“Compound interest” can be confusing in this context. A compound-interest savings calculator often models money growing when interest remains invested. A repayment calculator instead models interest accruing on debt between payments and uses amortization to estimate the payment that clears the balance. The mathematical relationship involves compounding, but it does not mean that the borrower’s entire original loan is charged interest anew each month.

When to Use the Estimate and How to Read It

Use the result to understand the mathematical effect of a stated principal, APR, and term. It can also help check a quoted payment or compare hypothetical combinations of inputs, provided the same assumptions and included costs are used. The result is not a lender’s offer or a determination of eligibility.

• Monthly payment is the modeled regular payment of principal and interest only.
• Total interest is the interest implied by making that rounded payment for every month in the term.
• Total payments can be found by adding the principal to total interest; in the example, that is $24,331.80.

A longer term generally spreads repayment across more installments, while a shorter term uses fewer installments. The formula recalculates the payment and total interest for the figures entered; it does not account for changes in income, cash flow, or other personal circumstances. Use the APR and term supplied in the lender’s documents rather than assuming that an advertised or illustrative figure applies to a particular loan.

Common Problems and Calculator Limits

The most frequent input error is entering a percentage incorrectly. Enter 8 for an APR of 8%, not 0.08: the calculator divides the percentage by 1200 to get the monthly decimal rate. Also check that the term is entered in years; this calculator converts it to months. Small rounding differences can occur because payments are shown to the nearest cent and an actual lender may use its own rounding and payment-allocation practices.

This formula is for a fixed-rate loan with regular, equal monthly payments. It does not accurately model a variable rate, interest-only period, irregular payment schedule, deferred interest, balloon payment, or a loan with fees added to the balance unless those features are separately represented in the inputs. It also assumes the entire stated principal is subject to the entered APR from the beginning.

Extra payments can reduce the balance sooner, but their effect depends on when they are made and how the lender applies them. This calculator has no extra-payment input, so its payoff date and interest total should not be treated as estimates for a loan with additional payments. For exact account figures, use the lender’s payment schedule or current payoff information.

Frequently Asked Questions

Does a loan repayment calculator use compound interest?
It models interest accruing periodically on the outstanding balance, using a monthly rate derived from APR. Scheduled payments reduce that balance over time; this is different from simply letting interest accumulate on an untouched original principal.

How do I calculate a monthly loan payment from APR?
Convert APR to a monthly decimal rate by dividing the percentage by 1200. Multiply the principal by that rate, then divide by one minus (one plus the monthly rate) raised to the negative number of monthly payments.

Why is the first payment mostly interest?
Interest for a payment period is based on the balance at its start. The initial balance is the largest, so the first payment has a larger interest portion than later payments on a standard amortizing loan.

Does total interest include fees or insurance?
No. This estimate includes modeled interest only. Fees, insurance, taxes, and other charges are excluded unless they are reflected in the principal or separately included in a lender’s quoted payment.

Why might my lender’s payment differ?
The quoted amount may include charges or use different timing, rounding, payment dates, rate details, or loan terms. Check the lender’s disclosure and payment schedule for the figures that apply to the actual loan.

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

Related

• Refinance a Personal Loan: Compare Payments and Interest
• Refinance a Personal Loan for a Lower Rate?
• Refinance Loan Financing for Personal Use: Costs & Payments

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