Loan Interest: Simple or Compound? Calculate the Cost

Loan interest can be calculated as simple or compound, depending on the loan’s terms and how unpaid interest is handled. This calculator estimates the monthly payment and total interest for a fixed-rate loan with equal monthly payments, using the amount, APR, and term you enter.

Formula

The calculator uses the standard fixed-payment amortization formula. It calculates a level monthly payment from the principal and monthly rate, then subtracts the original principal from all scheduled payments to estimate total interest.

• Monthly payment: P × r ÷ [1 − (1 + r)⁻ⁿ]
• Total interest: monthly payment × n − P

P is the loan principal in dollars, r is the monthly interest rate as a decimal (APR ÷ 1,200), and n is the number of monthly payments (years × 12). The APR input is a percentage per year. For this estimate, the unrounded payment formula is used in the expressions; displayed results are rounded to cents.

Worked Example

Using the defaults: a $20,000 loan, 8% APR, and a five-year term.

1. Convert APR to a monthly decimal rate: 8 ÷ 1,200 = 0.0066667.
2. Convert the term to payments: 5 × 12 = 60 months.
3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] ≈ $405.53 per month.
4. Calculate total interest from the unrounded payment: (monthly payment × 60) − $20,000 ≈ $4,331.80.

The displayed payment is $405.53. Because the calculator’s total-interest expression uses the formula’s unrounded payment rather than the cent-rounded display value, the example’s approximate total is $4,331.80. A lender’s actual payment schedule can differ through rounding and contract-specific details.

Assumptions

• The interest rate is fixed for the full term.
• Payments are equal, made monthly, and assumed to occur at the end of each period.
• Interest accrues monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

Is loan interest simple or compound?

There is no single answer for every loan. In everyday borrowing, a loan may be described as having simple interest when interest is calculated on the outstanding principal, while compounding means unpaid interest is added to the balance and can itself earn interest later. The agreement and its payment schedule determine how the balance changes.

For a typical fully amortizing installment loan, each scheduled payment covers interest accrued since the prior payment and reduces principal by the remainder. As principal falls, the interest portion generally falls too. This is not the same as charging interest repeatedly on the original loan amount, nor does the standard payment formula mean that the borrower pays compound interest on interest each month. If a payment is missed, deferred, or too small to cover accrued interest, however, unpaid interest may be treated differently under the contract.

How monthly loan payments work

At each payment date, the lender calculates interest based on the balance and applicable rate for the period. The payment is applied according to the loan terms; in a standard amortization schedule, the period’s interest is covered first and the remaining amount reduces principal. Early payments therefore tend to contain more interest because the balance is larger. Later payments tend to direct more toward principal.

For example, at an 8% nominal APR divided into monthly periods, the first month’s approximate interest on $20,000 is $20,000 × 0.08 ÷ 12, or $133.33. If the payment is about $405.53, roughly $272.20 goes toward principal in that first period. The amounts shift over time, while the scheduled payment stays level if the rate and terms stay unchanged.

Simple interest, compound interest, and APR

Simple interest is calculated on principal, often for each day or month that the balance is outstanding. An example of a simple-interest calculation over a fixed period is principal × annual rate × time, with time expressed in years. That shortcut may help estimate interest for a period, but it does not by itself calculate a multi-payment loan’s full amortization schedule.

Compound interest adds accrued interest to the balance, so future interest can be charged on that added amount. Compounding frequency matters: an annual rate compounded monthly does not produce exactly the same result as one compounded annually. APR is a rate stated on an annual basis; it should not be confused with the effective annual yield or with the total dollar cost. Fees may also affect a disclosed APR, depending on the product and applicable disclosure method. This calculator treats APR as the nominal annual rate divided by 12 and does not model fees.

What can change the actual cost?

The result is a mathematical estimate, not a payoff quote. Before comparing it with a loan document or account statement, check which balance, rate, dates, and charges are being used. Relevant differences can include:

• Variable rates: a rate change can alter the payment, the payoff date, or both.
• Fees and financed charges: amounts added to the balance can increase the amount on which interest accrues.
• Payment timing: daily accrual and actual payment dates may make period-by-period interest differ from a monthly approximation.
• Extra, missed, or late payments: these can change principal reduction, accrued interest, and the remaining schedule.
• Rounding: lenders may round each period’s interest and payment allocation, so totals can differ slightly from a formula using full precision.

For a precise balance or payoff amount, use the lender’s current statement or ask for an itemized payoff figure. The calculator does not include a separate input for compounding convention, fees, or irregular payments.

Common misconceptions

A common misconception is that every loan described as “simple interest” has interest computed only once on the amount first borrowed. In a simple-interest loan, interest can accrue repeatedly over time on the outstanding principal; regular payments reduce that principal, which changes subsequent interest. Another misconception is that APR alone tells you the total you will pay. The term, payment schedule, balance, fees, and any changes to the rate all matter.

Also, “compound” does not automatically mean a loan balance grows when payments are being made as agreed. A scheduled payment can cover accrued interest and reduce principal. Balance growth is possible when payments do not cover charges that accrue or when charges are added under the loan’s terms, but the exact treatment depends on the contract.

Frequently Asked Questions

Do personal loans use simple or compound interest?
It depends on the agreement and product. Many fixed-payment installment loans calculate periodic interest on the remaining balance, but you should check the note and payment schedule rather than infer the method from the loan category.

Is mortgage interest simple or compound?
Mortgage calculations commonly use periodic interest on the outstanding principal, with scheduled payments reducing the balance over time. Actual accrual conventions and payment handling depend on the loan documents and servicing.

Does paying extra reduce loan interest?
When an extra amount is applied to principal, it can lower the balance used to calculate later interest. The effect depends on how the lender applies the payment and whether the contract includes relevant charges or restrictions; confirm the allocation with the servicer.

Why is my first payment mostly interest?
Interest for the first period is calculated on the initial balance, which is usually larger than balances later in the schedule. The portion applied to principal increases as the balance declines, assuming equal payments and an unchanged rate.

Does this calculator show my exact loan cost?
No. It estimates a fixed-rate, equal-payment schedule and excludes fees, taxes, insurance, irregular payments, and lender-specific rounding. The lender’s disclosure and payment schedule give the exact figures for the loan.

This result is an estimate for educational purposes, 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