How Are Loans Calculated: Interest, APR, and Amortization

Loans are calculated by running three numbers through a formula: the principal you borrow, the interest rate the lender charges, and the term over which you repay. Which formula applies depends on the loan. A short personal loan may use simple interest. A mortgage or auto loan uses amortization, which keeps your monthly payment level while shifting the split between interest and principal. A credit line with a variable rate recalculates whenever its benchmark moves. How are loans calculated in each case comes down to picking the right formula and knowing which inputs the lender is allowed to change.

The Four Inputs Behind Every Loan

Every calculation starts with the same building blocks. Principal is the amount you actually receive. The interest rate is the percentage the lender charges for the use of that money. The term is how long you have to repay. And your credit score sets which rate you qualify for in the first place.

That last input moves the most money. On a $300,000 mortgage, a spread of roughly one percentage point between a strong-credit and weak-credit borrower translates to more than $70,000 in extra interest over the life of the loan. Scores above about 760 generally earn the best available rates; scores below 660 face noticeably steeper costs.

Compounding frequency is the quiet fourth lever. When interest compounds, the lender charges interest on both the principal and any accumulated unpaid interest. Monthly compounding, the standard for most consumer loans, applies that calculation twelve times a year rather than once. Two loans at identical stated rates can produce different totals if they compound on different schedules.

Simple Interest

The most direct loan math multiplies principal by annual rate by time in years. A $5,000 personal loan at 10% for one year generates $500 in interest ($5,000 × 0.10 × 1), for a total repayment of $5,500. Cut the term to six months and the time factor becomes 0.5, dropping the interest to $250.

Simple interest works for short-term, small-dollar products where the lender doesn’t compound during the term. You’ll see it on some retail financing offers and bridge loans. The appeal is that you know the total cost the day you sign.

Compound Interest

Most longer-term loans use compound interest, where any unpaid interest gets folded into the balance and starts generating interest of its own. The formula is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the time in years. A is what you would owe at the end if you made no payments at all.

Borrow $10,000 at 8% compounded monthly for five years with no payments, and the balance grows to about $14,898. The same loan compounded annually reaches roughly $14,693. That $205 gap comes entirely from how often the lender recalculates. The stated rate never changed. Federal law requires lenders to disclose compounding before you sign because of exactly this effect.

How Amortized Loans Work

Mortgages, auto loans, and most large installment loans use amortization. Your monthly payment stays the same, but the split between interest and principal shifts over time. Early on, most of your payment covers interest. As the balance shrinks, interest costs less each month, so a larger share of the same payment chips away at the debt itself.

The fixed-payment formula is M = P × [r(1+r)^n] / [(1+r)^n – 1], where M is the monthly payment, P is the loan amount, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments. On a $300,000 mortgage at 6.5% over 30 years, that produces a principal-and-interest payment of about $1,896. During the first month, roughly $1,625 of that goes to interest and only $271 reduces the balance. By year 20, those proportions have nearly reversed.

This front-loading is the most important thing to understand about amortized loans. Equity or ownership builds slowly at first. It also means extra payments in the early years pack an outsized punch: every additional dollar you put toward principal in year one saves you interest for the remaining 29 years.

When the Balance Grows Instead of Shrinks

Some loan structures allow payments that don’t even cover the monthly interest charge. The unpaid interest gets added to your principal, and you end up owing more than you originally borrowed. This is negative amortization, and it means you’re paying interest on interest while still writing a check every month.¹ Payment-option adjustable-rate mortgages that allow minimum payments below the interest amount are the most common place this appears. If a loan is advertising unusually low minimum payments, check whether those payments fully cover the monthly interest. If they don’t, the balance is going up.

Variable-Rate Recalculations

Not every loan locks in a single rate. Adjustable-rate mortgages and many private student loans tie the rate to a benchmark index that moves over time. The formula is straightforward: your rate equals the index value plus a fixed margin the lender sets at origination.² If the index is 4.0% and your margin is 2.75%, your rate is 6.75%.

The dominant benchmark for U.S. consumer loans is the Secured Overnight Financing Rate, or SOFR, which reflects actual overnight lending in the Treasury repurchase market.³ When SOFR moves, your rate adjusts at the next scheduled date, and your monthly payment is recalculated using the amortization formula at the new rate. Most adjustable-rate loans include caps limiting how far the rate can rise at each adjustment and over the life of the loan, but even with caps a rising-rate environment can push payments well above where they started.

What APR Measures That the Rate Doesn’t

The interest rate tells you the cost of borrowing the money. The Annual Percentage Rate rolls in origination fees, discount points, and certain closing charges to express the total annual cost as a single percentage. Two lenders can both quote 6.5% interest, but if one charges a 2% origination fee and the other charges nothing, their APRs differ. That’s the point of the number: it lets you compare offers that package costs differently.

Origination fees on personal loans commonly run from 1% to 10% of the amount borrowed, and lenders sometimes deduct the fee from your proceeds rather than adding it to the balance. Either way, the APR captures it. Federal law requires lenders to disclose the APR alongside the finance charge, amount financed, total of payments, and payment schedule on every closed-end consumer credit transaction.⁴

The disclosed APR has to be mathematically accurate within a narrow tolerance: no more than one-eighth of one percentage point above or below the correct rate for a standard transaction, or one-quarter of a point for an irregular one.⁵ A disclosed APR outside that tolerance gives the borrower grounds for a claim.

Totaling the Interest Yourself

You don’t need the APR formula to see what a loan actually costs in dollars. Multiply the fixed monthly payment by the number of payments, then subtract the original loan amount. A $20,000 auto loan at 60 payments of $400 totals $24,000, meaning $4,000 is interest. This works for any fixed-payment loan and is a fast way to gut-check a lender’s disclosure.

Paying Off Early

Paying a loan off ahead of schedule saves interest, but some loans charge a penalty for doing it. Federal law restricts those penalties on residential mortgages. A qualified mortgage, the standard category that covers most conventional home loans, can only impose a prepayment penalty during the first three years, capped at 3% of the outstanding balance in year one, 2% in year two, and 1% in year three.⁶ Adjustable-rate qualified mortgages and higher-priced loans cannot carry prepayment penalties at all.

Loans classified as high-cost mortgages under federal rules are flatly barred from carrying prepayment penalties. A mortgage lands in that category if, among other triggers, its terms would allow a penalty running beyond 36 months or exceeding 2% of the prepaid amount.⁷

For other consumer loans, watch for a related trap in the refund math. The Rule of 78s front-loads interest even more aggressively than standard amortization, making early payoff disproportionately expensive for the borrower. Federal law bans the Rule of 78s on any precomputed consumer loan with a term longer than 61 months; those loans must use a refund method at least as favorable as the actuarial method.⁸ Shorter-term loans can still use it, so if you plan to pay off a short personal loan early, ask which refund method applies.

The Tax Angle on Mortgage Interest

Interest on a home loan isn’t just a cost; part of it may reduce your federal income tax bill. If you itemize deductions, you can deduct mortgage interest on up to $750,000 of home acquisition debt ($375,000 if married filing separately).⁹ Debt taken out on or before December 15, 2017, still qualifies under the older $1 million limit.

The deduction applies to debt used to buy, build, or substantially improve a qualified home, including a second home. Interest on a home equity loan used for something else, like consolidating credit card debt or paying tuition, is not deductible.⁹ That changes the real cost comparison between a mortgage and other borrowing. A 6.5% mortgage with deductible interest costs less in practice than a 6.5% personal loan where none of the interest is deductible.

What the Lender Has to Show You

You don’t have to take a lender’s word on any of this. The Truth in Lending Act exists to force transparency, with the stated purpose of letting consumers compare credit terms across lenders and avoid uninformed borrowing.¹⁰ Every closed-end consumer loan must come with written disclosures of the APR, finance charge, amount financed, total of payments, and payment schedule before you’re bound to the contract.⁴

Regulation Z, which implements the Truth in Lending Act, requires that payment schedule to show the number, amount, and timing of your payments along with the total you’ll pay over the full term.¹¹ That’s different from a full amortization table showing the month-by-month split between principal and interest. Lenders commonly provide those tables as well, but the legal requirement is the schedule and the total cost. If the numbers on your disclosure don’t match the quote, or if the APR falls outside the permitted tolerance, that isn’t a rounding error. Lenders that fail to provide accurate disclosures face civil liability for statutory and actual damages plus attorney fees, with heightened exposure for violations tied to high-cost mortgages or the ability-to-repay rules.¹²

1
Consumer Financial Protection Bureau. What Is Negative Amortization
2
Consumer Financial Protection Bureau. For an Adjustable-Rate Mortgage (ARM), What Are the Index and Margin, and How Do They Work
3
Freddie Mac Single-Family. SOFR-Indexed ARMs
4
Office of the Law Revision Counsel. 15 USC 1638 – Transactions Other Than Under an Open End Credit Plan
5
eCFR. 12 CFR 226.22 – Determination of Annual Percentage Rate
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Office of the Law Revision Counsel. 15 USC 1639c – Minimum Standards for Residential Mortgage Loans
7
Consumer Financial Protection Bureau. 12 CFR 1026.32 – Requirements for High-Cost Mortgages
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Office of the Law Revision Counsel. 15 USC 1615 – Prohibition on Use of Rule of 78s in Connection With Mortgage Refinancings and Other Consumer Loans
9
Internal Revenue Service. Publication 936, Home Mortgage Interest Deduction
10
Office of the Law Revision Counsel. 15 USC 1601 – Congressional Findings and Declaration of Purpose
11
eCFR. 12 CFR 1026.18 – Content of Disclosures
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Office of the Law Revision Counsel. 15 USC 1640 – Civil Liability