Banks calculate interest on loans by plugging three numbers—your principal, your interest rate, and your loan term—into one of a few standard formulas: simple interest, amortized interest, or daily simple interest. Which formula the lender uses decides how much you pay in total and how each monthly payment is split between interest and principal. Personal loans often use simple interest, mortgages and most auto loans use amortization, and many credit unions run auto and personal loans on daily simple interest.
The Three Numbers Every Formula Starts With
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 to lend it to you. The loan term is how long you have to repay, in months or years. Federal law requires lenders to disclose all three, 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 rate (or “note rate”) is the raw percentage that goes into the interest formula. The annual percentage rate (APR) is broader: it rolls in origination fees, mortgage points, and other required charges to reflect the loan’s true yearly cost. Federal regulations require the APR to be calculated using either the actuarial method or the United States Rule, both of which account for when payments are made relative to what is still owed.2eCFR. 12 CFR 1026.22 – Determination of Annual Percentage Rate Two loans with the same nominal rate can carry different APRs if one bundles higher fees, so the APR is the more useful figure when comparing offers.
Simple Interest
Simple interest is the plainest formula. Interest is figured once on the original principal and does not change as you pay down the balance:
Interest = Principal × Annual Rate × Time in Years
On a $5,000 personal loan at 8% for two years, the math is $5,000 × 0.08 × 2 = $800. You owe $5,800 in total. The interest is locked in at signing; it does not shrink as the balance falls. Short-term personal loans and some auto financing use this method, calculating the full interest charge upfront and adding it to the principal.
One wrinkle: some lenders use a 360-day “banker’s year” instead of a 365-day calendar when they convert an annual rate into daily or monthly figures. A 360-day year gives a slightly higher daily rate because you are dividing by a smaller number. Your contract will state which convention applies.
Amortized Interest
Most mortgages and auto loans use amortization. Each monthly payment covers the interest that accrued on the current balance since your last payment plus a slice of principal. Because the balance drops after every payment, the interest portion shrinks month over month and the principal portion grows, even though the total payment stays the same.
The fixed monthly payment on an amortized loan comes from this formula:
Monthly Payment = P × [r(1 + r)n] / [(1 + r)n − 1]
Here, P is the principal, r is the monthly rate (annual rate divided by 12), and n is the total number of monthly payments. On a $300,000 mortgage at 6% for 30 years, r is 0.005 and n is 360. The formula returns a monthly payment of about $1,799. Total repayment lands near $647,500, meaning roughly $347,500 of that is interest.
The split inside each payment moves dramatically over the life of the loan. In month one, about $1,500 of the $1,799 goes to interest and only $299 chips away at principal. By the closing years, almost the whole payment is principal. Federal regulations define a “fully amortizing payment” as one that repays the whole loan over the stated term in substantially equal installments.3Consumer Financial Protection Bureau. 12 CFR 1026.43 – Minimum Standards for Transactions Secured by a Dwelling Lenders must disclose the 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 like amortization but tracks the balance day by day rather than month by month. The lender divides the annual rate by 365 to get a daily rate, then multiplies it by your current balance and the days since your last payment:
Daily Interest = (Annual Rate / 365) × Current Balance × Days Since Last Payment
Timing matters more under this method. On a $15,000 car loan at 5%, the daily charge runs about $2.05. A normal 30-day cycle produces roughly $61.50 in interest. Pay two days early and the interest drops to about $57.40; pay five days late and it rises to about $71.75. Credit unions and some auto lenders prefer this method because it reflects the true cost of delayed payments and rewards borrowers who pay ahead of schedule.
As with simple interest, check whether your contract divides the annual rate by 360 or 365 days. A 360-day divisor produces a slightly higher daily rate.
How Adjustable Rates Are Set
Fixed-rate loans use the same rate for the whole term. Adjustable-rate loans reset the rate on a schedule using a straightforward sum:
Interest Rate = Index + Margin
The index is a market benchmark that moves with economic conditions—the Secured Overnight Financing Rate (SOFR) and the prime rate are common choices. The margin is a fixed number of percentage points the lender adds, set at closing and locked 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 An index of 4% plus a margin of 2.5% gives you a 6.5% rate. When the index moves at your next adjustment date, your rate moves with it, capped by whatever limits your contract sets. Margins are negotiable at shopping time, so comparing them across lenders matters as much as comparing the starting rate.
Compounding and the Effective Annual Rate
Compounding is what happens when accrued interest is added to your balance and future interest is then charged on that larger amount. The more often it happens, the more you pay. The effective annual rate (EAR) 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) produces an EAR near 6.17%. Compounded daily (n = 365), the EAR climbs to about 6.18%. The gap looks trivial, but it matters on large balances over long terms. Most consumer installment loans compound monthly. Credit cards compound daily, which is one reason a carried balance gets expensive quickly. Federal law requires lenders to disclose the total finance charge so the dollar effect of compounding is visible before you borrow.5Office of the Law Revision Counsel. 15 USC Chapter 41 Subchapter I – Consumer Credit Cost Disclosure
How Extra Payments Cut Interest
On any amortized or daily-simple-interest loan, paying more than the minimum shrinks the balance faster and cuts the interest that accrues from that point forward. An extra $100 a month on a 30-year mortgage can shorten the term by years and save tens of thousands, because every dollar of principal you eliminate today wipes out all the interest that dollar would have generated for the rest of the loan.
Some lenders charge a prepayment penalty. Federal law limits them on residential mortgages: on a qualified mortgage, the penalty cannot exceed 3% of the outstanding balance in year one, 2% in year two, or 1% in year three, and no penalty is allowed after three years.6Office of the Law Revision Counsel. 15 USC 1639c – Minimum Standards for Residential Mortgage Loans High-cost mortgages under federal rules cannot carry any prepayment penalty at all.7Consumer Financial Protection Bureau. 12 CFR 1026.32 – Requirements for High-Cost Mortgages State law may add further limits, and federal credit unions cannot charge them at all. Check the prepayment clause in your loan agreement before you send in extra money.
What the Lender Has to Show You
The Truth in Lending Act requires lenders to give you standardized information about a loan’s cost 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 least:
- 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 as a percentage, accounting for payment timing and included fees.
- Total of payments: amount financed plus finance charge—what you will have paid when the loan is done.
- 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
On a mortgage, these figures appear on the Loan Estimate, delivered within three business days of application, and the Closing Disclosure, delivered at least three business days before closing. The Closing Disclosure breaks down how much of each payment goes to principal versus interest across the life of the loan. Regulation Z, which implements the Truth in Lending Act, standardizes the format so every lender presents the same information the same way.9Consumer Financial Protection Bureau. 12 CFR 1026.18 – Content of Disclosures If a number on your disclosure does not match what the formulas above would predict, ask the lender to walk through the calculation before you sign.