Three things determine the rate on offer, and knowing them explains most of the variation a household sees. The first is the general level of rates in the economy, which is the floor everything else is priced above and which moves with monetary policy and with what investors will accept for lending. The second is the term, because promising money for thirty years is a different commitment from promising it for six months. The third is the lender's assessment of the risk of not being repaid, which on consumer credit is what the credit report and score exist to price. This is why a mortgage secured by a house costs a fraction of what an unsecured card balance costs, and why the same borrower is quoted different rates by different lenders on the same day.
Here the subject becomes genuinely strange, and the strangeness is worth understanding because it explains disclosures that otherwise look inconsistent. Federal consumer law regulates this concept from two directions and only one of them bothers to define it. On the borrowing side, the Truth in Lending Act and Regulation Z never define interest at all. What they define is the finance charge, described as the cost of consumer credit as a dollar amount, and interest appears merely as the first item on a list of examples of it. On the saving side, Regulation DD does define it, for deposit accounts only, as any payment to a consumer or to an account for the use of funds in an account, calculated by applying a periodic rate to the balance.
That asymmetry is not an oversight. Interest alone was never the number Congress wanted borrowers to compare, because a lender can move cost out of the rate and into fees; so the credit side defines the broader finance charge and requires an all-in annual figure built from it. On the deposit side interest is the number being compared, so it is the thing defined. A reader who understands that stops expecting the two regimes to line up.
They do not line up, and the sharpest consequence is a collision of labels around the same three letters. On a loan, the annual percentage rate folds certain financing costs in alongside the interest rate, which is why the APR on a mortgage quote is usually a little above the quoted rate. On a deposit account, Regulation DD says the opposite: "Interest rate means the annual rate of interest paid on an account which does not reflect compounding," and it then permits that figure to "be referred to as the 'annual percentage rate' in addition to being referred to as the 'interest rate.'" The Truth in Savings Act says the same thing at statute. So on a deposit, "annual percentage rate" is a lawful label for the bare nominal rate with compounding stripped out, which places it below the account's annual percentage yield rather than above its rate. The all-in comparison figure exists on both sides; it is called APR on borrowing and APY on saving. Comparing an APR from one side of a balance sheet with an APR from the other is comparing two different kinds of number.
Regulation DD's definition also draws a boundary that catches people chasing a headline offer. A sign-up bonus is not interest: the regulation defines a bonus separately and expressly excludes such items, along with fee waivers and absorbed expenses, from the meaning of interest. So a bonus falls outside the yield calculation and is disclosed on its own.
Finally, two mechanics decide how much a given rate actually produces. Simple interest is charged on the original balance only. Compound interest is charged on the balance plus the interest already added, which is the engine of long-term saving and which does not switch off when it is pointed at a borrower instead. A tax asymmetry widens the gap between the two sides further. Interest you earn is gross income, and the IRS treats interest credited to an account you can withdraw from without penalty as taxable in the year it becomes available to you, though some interest, such as that on many municipal bonds, is tax-exempt. Interest you pay is different in kind: the tax code disallows a deduction for personal interest outright, and then carves specific categories back out of that definition, among them qualified residence interest on a home mortgage and interest on a qualified education loan. So the default on the paying side is no deduction, and the familiar exceptions are exceptions in the statute's own structure rather than in practice alone.