Your credit card charges 24.99% APR, and your savings account pays 5% APY. Those two percentages look like they speak the same language — but they don't. If you carry a $5,000 card balance for a full year, you will pay closer to 28% in effective interest, not 24.99%. And that 5% savings rate, compounded daily, quietly grows into 5.13% by year-end. The same "percent per year" means two different dollar amounts depending on which three-letter label sits next to it, and misunderstanding the difference costs borrowers real money while leaving savers comparing the wrong numbers.
APR and APY in One Paragraph
APR (annual percentage rate) is the annualized cost of borrowing: a simple-interest convention that spreads a loan's interest — and, for mortgages, certain upfront fees — across one year without accounting for compounding within that year. Lenders must disclose it under the Truth in Lending Act. APY (annual percentage yield) is the annualized return on saving: it starts from the nominal rate and folds in the effect of compounding, so it tells you exactly how much a deposit grows in a year. Banks must disclose it under the Truth in Savings Act. For the same nominal rate, APY is always equal to or higher than APR — equal only when interest compounds once a year, higher everywhere else.
Why APR Ignores Compounding
APR was designed to answer one question: which loan costs less? To make loans comparable across lenders, regulators defined APR as a standardized yearly rate built on simple interest. It deliberately leaves intra-year compounding out of the math, because its job is comparison, not prediction of your exact finance charge.
What APR includes instead: fees
For mortgages, the APR is broader than the interest rate. The Consumer Financial Protection Bureau explains that APR reflects the interest rate plus points, mortgage broker fees, and other charges you pay to get the loan — which is why your APR is usually higher than your note rate. A 7.00% rate with two discount points might carry a 7.20% APR, while a 7.10% no-fee loan shows 7.10%. The APR lets you compare those two offers on one scale.
That fee-spreading comes with a catch: APR amortizes upfront costs over the full loan term. If you sell or refinance after five years, the true cost of the fee-heavy loan is higher than its APR suggests, because you paid 30 years' worth of spread-out fees for five years of borrowing.
Where compounding sneaks back in: credit cards
Credit card APRs look like simple interest but behave like compound interest. The issuer divides your APR by 365 to get a daily periodic rate, applies it to your balance each day, and adds the resulting interest to the balance — so tomorrow's interest is charged on today's interest. The CFPB notes that many issuers compound daily, which means a carried balance grows faster than the APR alone implies. A 24.99% APR compounded daily works out to an effective rate of about 28.4% over a full year. The APR is still the right number for comparing two cards; it is just not the number that determines what a year of revolving actually costs you.
Auto loans and most personal loans sit in the middle: interest typically accrues on the declining balance with monthly compounding, so the gap between APR and effective cost is smaller than on a credit card but still nonzero.
Why APY Includes Compounding
APY was designed to answer the mirror-image question: if I leave my money here for a year, how much more will I have? Because deposit accounts credit interest that itself starts earning interest, the only honest answer bakes compounding in. That standardization is the point of the Truth in Savings Act: without it, banks could advertise the same nominal rate while compounding at different frequencies, and shoppers would have no way to compare.
The formula
For a nominal rate r compounded n times per year:
APY = (1 + r/n)^n - 1
A 5% nominal rate compounded daily gives (1 + 0.05/365)^365 - 1, which is about 5.13%. The same 5% compounded monthly gives about 5.12%, and compounded annually gives exactly 5.00%. Regulators use an equivalent form based on actual interest earned over the term, but the intuition is identical: more frequent compounding means interest starts earning its own interest sooner, so the yield edges up.
The dollar difference on savings
On a $10,000 deposit at a 5% nominal rate for one year:
- Annual compounding: $500.00 of interest
- Monthly compounding: about $511.62
- Daily compounding: about $512.68
At savings-account rates the frequency gap is a dozen dollars — nice, not life-changing. But the gap grows with the rate, which is exactly why the same math matters so much more on the borrowing side, where rates run four to five times higher.
How to Compare Loans Correctly
Compare APR to APR, never APR to APY. A 7% mortgage APR and a 5% savings APY measure different things; subtracting one from the other produces nonsense. Within borrowing, keep comparisons like-for-like:
- Same loan type and term. A 30-year fixed APR assumes 30 years of payments. Comparing it to a 15-year APR, or a fixed-rate APR to an adjustable-rate APR, mixes different horizons and different rate behavior. The CFPB specifically warns that an ARM's APR does not reflect the loan's maximum possible rate.
- Match the APR to your actual horizon. Because APR spreads fees over the full term, the lowest-APR mortgage is only the cheapest if you keep the loan long enough. If you expect to refinance or move in three to five years, ask each lender for the total cost — payments plus closing costs — over your horizon instead.
- Know what the APR leaves out. Some closing costs are excluded from the APR calculation, and a home equity line's APR excludes fees that a closed-end loan's APR includes, so cross-type comparisons mislead.
- For credit cards, the APR ranks offers but understates revolving cost. If you pay in full every month, the APR barely matters — grace periods mean you pay no interest at all. If you revolve, the daily periodic rate and daily compounding determine the real damage, and a lower-APR card still wins.
- For very short-term credit, annualize with care. A $15 fee on a $100 two-week advance annualizes to nearly 400% APR. That number is mathematically honest — it is what the cost would be if repeated all year — but for a one-time bridge, the total finance charge in dollars is the more useful comparison.
How to Compare Savings Correctly
Compare APY to APY — frequency is already handled. A 4.60% APY compounded monthly beats a 4.55% APY compounded daily, full stop. You never need to adjust for compounding yourself; that adjustment is what the APY is. But the APY is only the headline. Check what sits behind it:
- Balance tiers and caps. Many accounts pay the advertised APY only above a minimum balance, or only up to a cap, with a near-zero rate beyond it. A 5.00% APY capped at $5,000 earns less on a $25,000 balance than a tier-free 4.60%.
- Teaser rates. Some APYs are introductory bonuses that expire after a few months. Read the disclosure for the ongoing rate, not just the headline.
- Fees that eat the yield. Monthly maintenance fees on a small balance can erase the entire APY. A fee-free 4.40% account beats a 4.60% account with a $12 monthly fee on balances under $10,000.
- Variable rates. Savings APYs float with the market. Today's best APY can drift within months, so re-check periodically rather than assuming the ranking holds.
- Taxes. Deposit interest is taxed as ordinary income. In a 24% bracket, a 5.00% APY keeps about 3.80% after tax. That doesn't change which account wins, but it changes whether parking cash beats paying down a 7% loan — it usually doesn't.
Common Mistakes That Cost Real Money
Comparing a loan's APR directly to a savings APY. "Borrow at 7%, earn 5%, net cost 2%" understates the borrowing side, because the loan compounds against you while fees hide inside the APR. Run both sides in dollars over the same horizon instead.
Chasing the highest APY while ignoring tiers and fees. The top advertised yield often comes with balance games or fees that make the second-best offer better for your actual balance. Multiply, don't headline-shop.
Picking the lowest mortgage APR when you'll move soon. Paying two points to shave 0.25% off your rate is a good deal over 30 years and a bad one over four. Divide the upfront cost by the monthly savings to find your break-even month — if it lands after your expected move, take the higher rate with lower fees.
Assuming 0% APR means free. Promotional 0% offers often carry balance-transfer fees of 3–5%, and deferred-interest versions retroactively charge full interest if any balance remains when the promo ends. Read the "what happens at month 19" clause before you celebrate month one.
Ignoring compounding frequency on revolving debt. Minimum-payment math at 24.99% APR already looks grim; daily compounding makes it slightly worse, and it means every extra principal dollar you pay today stops compounding against you immediately. That is the real argument for paying more than the minimum whenever you can.
Keep Your Interest Straight from Day One
Every loan payment you make is quietly two transactions — part principal, part interest — and every savings deposit earns interest that is itself taxable income. Recording those pieces separately, rather than as single lump sums, is what makes your books tell the truth about what borrowing costs you and what your cash earns. Beancount.io provides plain-text accounting that gives you complete transparency and control over your financial data — no black boxes, no vendor lock-in. Get started for free and see why developers and finance professionals are switching to plain-text accounting.
