Interest Rates: APR vs APY

APR — Annual Percentage Rate

APR is the yearly interest rate without factoring in intra-year compounding. A credit card with a 21% APR charges 21% per year — but interest is actually compounded monthly at 21/12 = 1.75% per month, so if you carry a balance all year, you pay closer to 23.1% in effective interest.

APR is the standard for loans, credit cards, and mortgages. U.S. law (Truth in Lending Act) requires lenders to disclose APR in standardized form so borrowers can compare offers. For loans, APR typically includes certain fees and closing costs built in, so a loan with a nominal 6% rate and $5,000 in fees might be disclosed as a 6.3% APR.

APY — Annual Percentage Yield

APY (also called EAR, Effective Annual Rate) includes the effect of compounding within the year. A savings account paying 5% APR compounded monthly pays an APY of:

(1 + 0.05/12)^12 − 1 = 5.12%

The more frequent the compounding, the larger the gap between APR and APY. Daily compounding at 5% gives an APY of about 5.13%; continuous compounding gives 5.127%.

APY is the standard for savings accounts, CDs, and money market accounts. Banks are required to disclose APY for deposit accounts.

Why it matters

A 5% APY savings account isn't the same as a 5% APR savings account. The APY is 5% flat; the APR 5% account, compounded monthly, yields 5.12% APY. When comparing, always convert both to the same basis.

On the loan side, two loans with the same APR can cost different amounts if one has more frequent compounding or higher fees. Many credit cards use daily compounding, which is why "average daily balance" shows up in statements.

The loan case: APR includes fees

For mortgages specifically, the APR is designed to let you compare loans with different rate and fee combinations on equal footing. Two offers:

• Offer A: 6.0% rate, $0 closing costs
• Offer B: 5.75% rate, $6,000 closing costs

Offer B has a lower rate but upfront fees. The APR rolls those fees into the effective rate over the life of the loan, so you can see that (for example) Offer B is effectively 5.88% APR. Now you can compare 6.0% to 5.88% directly.

Worth noting: APR assumes you hold the loan to term. If you refinance or sell early, the fee-heavy loan actually costs more than its APR suggests.

Rate vs APR confusion

Mortgage offers typically show both:

• "Rate" is the stated interest rate. That's what determines your monthly payment.
• "APR" is the rate including fees and closing costs.

If APR is significantly higher than rate, it means the loan has meaningful fees. If they're close, fees are minimal.

How Horizons uses this

Horizons uses APR as the liability interest rate. If you enter 6.0% as the rate on a mortgage, the engine computes monthly interest as (balance × 0.06 / 12) and amortizes correctly. For savings accounts and investments, we report returns as annualized equivalents, typically as APY with monthly compounding assumed.