Banks calculate interest on loans by plugging three numbers — the principal, the interest rate, and the loan term — into one of a few standard formulas: simple interest, amortized interest, or daily simple interest. Which formula your lender uses determines how much you pay over the life of the loan and how each monthly payment is divided between interest and principal. Once you know which formula applies to your loan, you can reproduce the lender’s math, predict your total cost, and see exactly what an extra payment would save you.
The Three Numbers Behind Every Calculation
Every interest formula starts with the same inputs. The principal is the amount of credit you actually receive, sometimes labeled “amount financed” on your paperwork. The interest rate is the annual percentage the lender charges for the use of that money. The loan term is how long you have to repay, stated in months or years. Federal law requires lenders to disclose all three of these figures, along with the total finance charge and the total of all payments, before you sign.1Office of the Law Revision Counsel. 15 USC 1638 – Transactions Other Than Under an Open End Credit Plan
Your loan documents will show two rates. The nominal interest rate (sometimes called the note rate) is the base cost of borrowing and the number that goes directly into the interest formulas below. The annual percentage rate (APR) is broader: it folds in certain upfront costs such as origination fees and mortgage points to give a fuller picture of the loan’s yearly cost. Federal regulations require lenders to calculate the APR using either the actuarial method or the United States Rule method, both of which account for the timing of payments relative to the amount borrowed.2eCFR. 12 CFR 1026.22 – Determination of Annual Percentage Rate When you compare offers, the APR is the more useful figure, because two loans with the same nominal rate can have different APRs if one carries higher fees.
Simple Interest
Simple interest is the most straightforward method. Interest is calculated once on the original principal and doesn’t change as you make payments.
Interest = Principal × Annual Rate × Time (in years)
Take a $5,000 personal loan at 8% for two years. The math is $5,000 × 0.08 × 2 = $800, so you would owe $5,800 in total. The interest amount is locked in from the start and doesn’t shrink as you pay down the balance. Short-term personal loans and some auto financing use this method, calculating the full interest charge upfront and adding it to the principal.
One detail affects the calculation more than it looks like it should: some lenders use a 360-day “banker’s year” instead of a 365-day calendar year when converting an annual rate to a daily or monthly figure. Dividing by 360 produces a slightly higher daily rate and a slightly higher total interest charge. Your contract will name the convention that applies.
Amortized Interest
Most mortgages and auto loans use amortized interest. Each monthly payment covers two things: the interest that has accrued since your last payment and a slice of the principal. Because the interest charge recalculates every month against your current outstanding balance, more of each payment goes to principal and less to interest as the balance falls.
The standard formula for the fixed monthly payment on an amortized loan is:
Monthly Payment = P × [r(1 + r)n] / [(1 + r)n − 1]
P is the principal, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. On a $300,000 mortgage at 6% over 30 years, the monthly rate is 0.005 and n is 360. Running the formula gives a monthly payment of roughly $1,799. Over the full 30 years, you would pay about $647,500, which means roughly $347,500 goes to interest alone.
The split inside those payments shifts dramatically over time. In month one, about $1,500 of the $1,799 payment goes to interest and only $299 or so reduces the balance. By the final years, almost the entire payment goes to principal. Federal regulations define a “fully amortizing payment” as one that will repay the entire loan amount over the stated term using substantially equal monthly installments.3Consumer Financial Protection Bureau. 12 CFR 1026.43 – Minimum Standards for Transactions Secured by a Dwelling Lenders are required to disclose your full payment schedule so you can see this shift before closing.1Office of the Law Revision Counsel. 15 USC 1638 – Transactions Other Than Under an Open End Credit Plan
Daily Simple Interest
Daily simple interest works on the same principle as amortized interest but tracks charges down to the exact day rather than the month. The lender divides the annual rate by 365, then multiplies that daily rate by your current outstanding balance and the number of days since your last payment.
Daily Interest Charge = (Annual Rate / 365) × Outstanding Balance × Days Since Last Payment
On a $15,000 car loan at 5%, the daily interest charge is about $2.05. A normal 30-day cycle produces roughly $61.50 in interest that month. Pay two days early and it drops to about $57.40. Wait five days past the due date and it climbs to about $71.75. Credit unions and some auto lenders favor this method because it rewards early payments and reflects the true cost of late ones. Check whether your contract divides the annual rate by 360 or 365; the 360-day divisor produces a slightly higher daily rate.
How Adjustable Rates Are Set
Fixed-rate loans use the same rate for every calculation until the loan is paid off. Adjustable-rate loans recalculate the rate periodically using a simple sum:
Your Interest Rate = Index + Margin
The index is a benchmark rate that moves with market conditions, such as the Secured Overnight Financing Rate (SOFR) or the prime rate. The margin is a fixed number of percentage points the lender adds on top; it’s set in your loan agreement at closing and stays the same for the life of the loan.4Consumer Financial Protection Bureau. For an Adjustable-Rate Mortgage (ARM), What Are the Index and Margin, and How Do They Work If the index sits at 4% and your margin is 2.5%, your rate is 6.5%. When the index moves at the next adjustment period, your rate moves with it, subject to any rate caps in the contract. Because the margin is negotiable when you shop, comparing margins across lenders matters as much as comparing the initial rate.
Compounding and the Effective Annual Rate
Compounding means accrued interest is added to your balance, and future interest is then charged on that larger amount. How often this happens changes the total you pay: the more frequent the compounding, the higher the real cost.
The effective annual rate (EAR) captures this effect and lets you compare loans with different compounding schedules on equal footing:
EAR = (1 + r/n)n − 1
r is the nominal annual rate and n is the number of compounding periods per year. A 6% nominal rate compounded monthly (n = 12) has an EAR of about 6.17%. Compounded daily (n = 365), the same rate produces an EAR of about 6.18%. The gap is small on a single loan but grows on large balances over long terms. Most consumer installment loans (mortgages, auto loans) compound monthly. Credit cards typically compound daily, which is one reason a carried balance gets expensive. Federal law requires lenders to disclose the total finance charge so you can see the full dollar impact of compounding before you borrow.5Office of the Law Revision Counsel. 15 USC Chapter 41 Subchapter I – Consumer Credit Cost Disclosure
How Extra Payments Cut Your Interest
On any amortized or daily-simple-interest loan, paying more than the minimum reduces the outstanding balance faster, which means less interest accrues from that point forward. An extra $100 a month on a 30-year mortgage can shave years off the term and save tens of thousands in interest, because every dollar of extra principal eliminates future interest charges that would have compounded over the remaining life of the loan.
Some lenders charge a prepayment penalty. Federal law limits these on residential mortgages. For a qualified mortgage, any prepayment penalty must phase out over three years: no more than 3% of the outstanding balance in the first year, 2% in the second, and 1% in the third. After three years, no penalty is allowed.6Office of the Law Revision Counsel. 15 USC 1639c – Minimum Standards for Residential Mortgage Loans Loans classified as “high-cost mortgages” under federal rules cannot include any prepayment penalty at all.7Consumer Financial Protection Bureau. 12 CFR 1026.32 – Requirements for High-Cost Mortgages State laws may add more limits, and some lenders, such as federal credit unions, cannot charge prepayment penalties at all. Check your agreement for a prepayment clause before making extra payments.
What the Lender Has to Show You
The Truth in Lending Act requires lenders to give you standardized information about the cost of borrowing so you can compare offers across institutions.8Office of the Law Revision Counsel. 15 USC 1601 – Congressional Findings and Declaration of Purpose For a closed-end loan (most mortgages, auto loans, and personal loans), the lender must disclose at minimum:
- Amount financed: the actual dollar amount of credit you receive.
- Finance charge: the total dollar cost of borrowing, including interest and certain fees.
- Annual percentage rate: the yearly cost of credit expressed as a percentage, accounting for the timing of payments and included fees.
- Total of payments: the sum of the amount financed and the finance charge, which is what you will have paid when the loan is fully repaid.
- Payment schedule: the number, amount, and timing of every payment.1Office of the Law Revision Counsel. 15 USC 1638 – Transactions Other Than Under an Open End Credit Plan
For mortgage loans, these figures appear on the Loan Estimate (provided within three business days of applying) and the Closing Disclosure (provided at least three business days before closing). The Closing Disclosure includes a detailed breakdown showing how much of each payment goes to principal versus interest over time. Regulation Z, which implements the Truth in Lending Act, standardizes the format so every lender presents the information the same way.9Consumer Financial Protection Bureau. 12 CFR 1026.18 – Content of Disclosures If a number on your disclosure doesn’t match what you’d expect from the formulas above, ask your lender to walk through the calculation before you sign.