Questions: APR vs. APY and Interest Rate Calculation

Question 1

Bank A offers a savings account with 6% APR compounded monthly. Bank B offers 5.9% APY. Which provides a better annual return?

• A. Bank A, because 6% is greater than 5.9%
• B. Bank B, because APY already includes compounding and is the correct basis for comparison
• C. Bank A, because monthly compounding produces more interest than annual compounding
• D. They are equivalent — APR and APY represent the same rate expressed differently

Answer: (B)

Bank A's 6% APR compounded monthly converts to APY = (1 + 0.06/12)^12 − 1 ≈ 6.17%. Since Bank B's APY of 5.9% is lower than 6.17%, Bank A is actually better. The trap in option A is comparing the stated rates directly (6% vs. 5.9%) without converting to the same basis. APY is the correct comparison because it captures the full effect of compounding — always compare APYs when evaluating savings accounts.

Question 2

A credit card advertises a 20% APR. Why might advertising APR rather than APY be considered favorable to the lender?

• A. APR and APY are equal for credit cards, so the choice doesn't affect the apparent rate
• B. When interest compounds more than once per year, APY > APR, so advertising APR makes the rate appear lower than the true annual cost
• C. APY is more complex to compute and would confuse consumers
• D. APR is a universal international standard while APY varies by country

Answer: (B)

When interest compounds more frequently than once per year (daily on most credit cards), APY > APR. A 20% APR compounded daily converts to APY ≈ 22.1%. Advertising the lower APR number makes the product appear cheaper than it truly is. This asymmetry is why savvy borrowers convert APR to APY — the advertised rate systematically understates the true annual cost when compounding is frequent.

Question 3

For a savings account with a fixed nominal rate, more frequent compounding always results in a higher APY.

• T. True
• F. False

Answer: True

APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. As n increases, this expression increases monotonically (approaching e^(APR) at continuous compounding), which is always greater than the simple APR. Daily compounding always yields a higher APY than monthly compounding at the same APR, which yields higher than annual compounding. The effect shrinks as n grows large, but APY is always at least as large as APR.

Question 4

Two savings accounts with the same APY but different compounding frequencies will produce different year-end balances.

• T. True
• F. False

Answer: False

APY already accounts for compounding frequency — that's its purpose. If two accounts have the same APY, they produce the same annual return by definition, regardless of how often they compound. APY is the effective annual rate after compounding is factored in. This is exactly why APY is the right number to compare: it strips away compounding frequency differences so accounts can be evaluated on equal footing.

Question 5

Why is APY the better number to use when comparing savings accounts, even though APR is what lenders typically advertise?

Model answer: APY includes the full effect of compounding over a year, showing what you actually earn. APR simply multiplies the periodic rate by the number of periods without accounting for compounding — it ignores the fact that interest compounds on itself. Two accounts with the same APR but different compounding frequencies will have different APYs and produce different balances. Comparing APYs gives a consistent, apples-to-apples view of actual annual returns regardless of compounding schedule.

The formula APY = (1 + APR/n)^n − 1 converts any APR and compounding frequency into a single comparable number. An account with 5% APR compounded monthly has APY ≈ 5.12%, while one compounded daily has APY ≈ 5.13%. These are small at low rates but grow at higher rates. The same logic applies to borrowing: always convert loan APRs to APY to see the true annual cost — the advertised APR is almost always lower than what you actually pay.