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The Difference
APR (Annual Percentage Rate) is the simple annual interest rate without accounting for compounding. It's what lenders advertise. "0% APR for 12 months" means you pay 0% per year, calculated simply.
APY (Annual Percentage Yield) is the effective annual rate accounting for compounding. If interest compounds monthly, APY is higher than APR.
For savings and investments, APY is better (you earn more). For borrowing, APR is often quoted, but APY is what you actually pay.
How Compounding Works
Simple interest (APR model): Borrow $10,000 at 10% APR simple interest. Interest per year: $1,000. If paid back after 1 year, you owe $11,000. If paid back after 2 years with no payments, you owe $12,000 (simple interest doesn't compound).
Compound interest (APY model): Borrow $10,000 at 10% APR compounded monthly.
- Month 1: $10,000 × (10% ÷ 12) = $83.33 interest. Balance: $10,083.33
- Month 2: $10,083.33 × (10% ÷ 12) = $84.03 interest. Balance: $10,167.36
- ...
- Year 1: Balance: $10,471.23
- Year 2: Balance: $10,975.67
With simple interest, you'd owe $12,000. With compounding, you owe $10,975.67. Wait—that's less?
Actually, the direction reverses based on whether you're earning or paying:
- Earning interest on savings: Compound interest is your friend. It helps you earn more.
- Paying interest on debt: Compound interest is your enemy. It makes you owe more.
APR vs. APY: The Savings Account Lens
A high-yield savings account advertises: "4.5% APY."
This means if you deposit $10,000, you earn:
- Year 1: $10,000 × 0.045 = $450 earned
- Year 2: $10,450 × 0.045 = $470.25 earned (compounding)
- Total after 2 years: $10,920.25
The APY already accounts for compounding. You earn exactly 4.5% compounded annually.
If they quoted "4.5% APR compounded monthly," the effective APY would be:
APY = (1 + 0.045/12)^12 - 1 = 4.60%
So "4.5% APR monthly" is actually "4.60% APY." This is why APY is the standard for savings—it's honest about what you'll actually earn.
APR vs. APY: The Borrowing Lens
A credit card advertises: "20% APR."
What do you actually owe?
If you borrow $5,000 and don't make payments for one year:
With simple interest (APR model): Interest owed: $5,000 × 0.20 = $1,000 Total owed: $6,000
With compound interest (APY model, monthly compounding): APY = (1 + 0.20/12)^12 - 1 = 21.94% Interest owed: $5,000 × 0.2194 = $1,097 Total owed: $6,097
The difference: $97 on a $5,000 balance. Over years of credit card debt, this compounds significantly.
Real-World Example: The Mortgage Difference
Mortgage at 6% APR, 30 years, $400,000 principal.
Monthly payment: $2,398.20 Total paid over 30 years: $863,352 Total interest: $463,352
Now, quote the same loan as "6% APR compounded monthly," which is "6.17% APY."
Monthly payment: $2,436.24 Total paid over 30 years: $876,649 Total interest: $476,649
The difference: $13,000+ over the life of the loan from how interest is quoted.
(Note: Mortgages are typically quoted as APR with monthly payments, not APY, so the first calculation is standard. But the concept stands.)
How to Compare Loans
When comparing loans, use APY (or request the lender calculate it). APR alone is misleading if compounding frequency differs.
Example:
- Loan A: 10% APR, compounded monthly = 10.47% APY
- Loan B: 10.5% APR, compounded annually = 10.5% APY
Loan A looks cheaper (lower APR) but costs the same (equal APY). Always ask for APY or calculate it yourself.
Formula to convert APR to APY: APY = (1 + APR/n)^n - 1
Where n = compounding periods per year (12 for monthly, 365 for daily).
The Impact Over Time
Credit card debt: $5,000 balance at 20% APR, only making minimum payments ($100/month):
- Total interest paid: $2,160
- Total time: 56 months (4.7 years)
- Effective cost: 43% of the original balance paid in interest alone
This is why minimum payments are so destructive. Interest compounds monthly, and you're barely touching principal.
Mortgage rate difference: $400,000 mortgage, 30 years:
- 5% APR: $2,147.29/month, $773,435 total
- 6% APR: $2,398.20/month, $863,352 total
- 7% APR: $2,661.21/month, $957,636 total
A 1% rate increase costs $89,884 over 30 years. A 2% increase costs $184,201.
Savings account difference (opposite effect): $20,000 balance for 30 years:
- 0.5% APY: $28,099 (earned: $8,099)
- 2% APY: $32,233 (earned: $12,233)
- 4% APY: $69,023 (earned: $49,023)
A 3.5% APY difference over 30 years almost doubles your savings.
How Compounding Frequency Matters
Higher compounding frequency = more frequent calculation of interest = higher effective cost (on debt) or yield (on savings).
10% APR under different compounding:
- Annually: 10.00% effective
- Semi-annually: 10.25% effective
- Quarterly: 10.38% effective
- Monthly: 10.47% effective
- Daily: 10.52% effective
The difference compounds over time. On $10,000 debt for 5 years at 10% APR:
- Annual compounding: ~$16,289 owed
- Daily compounding: ~$16,487 owed
- Difference: $198
Small, but it adds up. This is why credit card issuers use daily compounding (they want to maximize interest owed) while savings accounts use daily or monthly (to seem more generous).
How to Use This Information
When borrowing:
- Ask for APY, not just APR.
- Compare total cost, not just rate. A 0% APR car loan for 5 years might cost more than a 5% APR loan for 3 years (longer term = more interest in total).
- Understand compounding frequency. Daily compounding is worse for you (as a borrower) than monthly.
When saving:
- Look for APY, not APR.
- Compounding frequency helps you. Daily or monthly compounding is better than annual.
- Small APY differences matter over decades. 4.5% vs. 3.5% APY over 30 years is ~$15,000 on a $20,000 deposit.
A Worked Example
You're deciding between two credit cards:
Card A: 18% APR, monthly compounding Effective APY: 19.56%
Card B: 19% APR, daily compounding Effective APY: 20.91%
Card B's APR is 1% higher, but the APY difference is 1.35%.
On a $5,000 balance you carry for 1 year:
- Card A: Interest owed: $975
- Card B: Interest owed: $1,045
- Difference: $70
Small on $5,000, but if you carry debt regularly, these differences compound.
The Takeaway
APR is a simplified headline. APY is reality. Always ask for and compare APY when borrowing or saving. And remember: small percentage differences compound massively over decades.
A mortgage rate that's 1% lower over 30 years saves you $100,000+. A savings rate that's 1% higher over 30 years earns you $50,000+.
Compounding is your friend (on savings) or enemy (on debt). Know which direction it's working.
