APR vs APY: The Difference, With a Worked Example | Cash Book

Most people use APR and APY as though they were two spellings of one word. They are not. And the slip only ever runs one way: people say APR when they mean the return on their savings, while nobody in the history of credit has looked at a card statement and called the 22 percent an APY. Borrowing has the louder vocabulary. So it lends its word to everything.

APR is the annual percentage rate, the yearly cost of borrowing expressed as one figure that includes interest and certain fees required as a condition of the credit; APY is the annual percentage yield, the yearly return on money you hold, stated after the effect of compounding. One is a price. The other is a return. They are computed under different rulebooks, and no arithmetic converts one into the other.

The price you pay

APR exists because a bare interest rate hides things. A loan advertised at 6 percent with a 400 arrangement fee costs more than a loan at 6.5 percent with no fee, and the headline rates tell you the exact opposite, which is the whole reason regulators went to the trouble of defining a single number with the required charges folded into it. In the United States the calculation is prescribed by Regulation Z; in the United Kingdom and the European Union, equivalent rules govern how credit is advertised.

Two cautions come with it.

APR describes a rate, not a total. A five-year and a two-year loan at the same APR do not cost the same. The longer one carries a balance longer. Judging a loan on its APR alone is how people end up surprised by the total amount payable, which sits in the pre-contract documents and is usually the figure printed smallest.

Representative APR is not a promise either. It is the rate the lender expects at least 51 percent of accepted applicants to get, which leaves up to 49 percent of them being offered something worse, so read it as a number the marketing department is permitted to print rather than as anything resembling an offer. The offer arrives after assessment.

Credit cards add a wrinkle on top. Purchase, cash advance and balance transfer APRs usually differ, and interest on cash advances typically starts immediately rather than after a grace period.

The arithmetic behind 12.68 percent

APY answers a narrower question. If a nominal rate is paid in instalments during the year, and each instalment starts earning too, what is the effective annual return?

APY = (1 + r/n)^n − 1

where r is the nominal annual rate and n is the number of compounding periods per year.

Take a nominal 12 percent compounded monthly. The monthly rate is 0.12 divided by 12, or 0.01, so the calculation is 1.01 to the twelfth power, minus one. That is 1.126825 minus one, or 12.68 percent. On 1,000 held for a year, simple 12 percent pays 120 and monthly compounding pays 126.83. The extra 6.83 is interest earned on interest.

Frequency matters less than people expect, and this is where a certain kind of saver loses an afternoon comparing accounts: the same nominal 12 percent compounded quarterly gives 12.55 percent, daily gives 12.7475 percent, and continuous compounding, the theoretical limit, gives 12.7497 percent. Annual to monthly is worth having. Monthly to daily is rounding.

In the United Kingdom the same idea is published as AER, the annual equivalent rate, so that an account paying monthly and an account paying annually can be compared honestly. In the United States, APY is defined under the Truth in Savings rules and must be quoted on deposit advertising.

Which side is bigger

The practical conclusion is unglamorous. For most households the rate on savings is a small lever and the rate on debt a large one, because the balances are lopsided. Earning 4 percent APY on 2,000 of savings is 80 a year. Paying 22 percent APR on 2,000 of card debt is around 440 a year. Same balance. Five and a half times the money.

That is why the ordering in most public guidance runs: keep a small cash buffer, clear expensive debt, then build savings. The emergency fund entry covers the buffer, the emergency fund calculator sizes it against your monthly costs, and the debt payoff calculator shows what an extra monthly amount does to the finish date and to the interest total.

Rates move slowly and are capped by whatever the market happens to be offering. Balances move this month. None of this is advice about your situation; if the numbers are large or the debt is in difficulty, a regulated debt adviser is the right person to talk to.

Every one of those calculations needs the same input, which is an honest figure for what you spend in a month. No rate can give you that.

The monthly number, and where it comes from

Cash Book does not calculate interest and never connects to a bank. APR and APY live on your statements, not in the app. What the app holds is the number those decisions depend on.

Set up an account for each place money sits, a card included, and the Accounts screen shows one net-worth figure over the cards, so a falling card balance reads as a rising total. Insights puts six months of income against expense bars, which is where you see whether there is genuinely a surplus to point at a balance, and the monthly budget guide covers building a plan around that surplus; the 50/30/20 rule is one starting shape, with its 20 percent aimed at savings and debt reduction.

That leaves the boring precondition. The monthly figure has to be real, which means logging has to be fast enough that you keep doing it: the expense tracking guide covers the habit, and the quick keypad is three taps. Read those two if your month is currently a guess. If it is not a guess, you already hold everything these conversations need.

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