How to Calculate APY: Formula, Examples & Calculator Guide 2026

You're comparing savings accounts and see two options: Bank A offers "5.0% interest compounded daily" and Bank B offers "5.05% APY." Which one earns more? Surprisingly, they might be exactly the same – if you know how to calculate APY.

APY (Annual Percentage Yield) is the true annual return you earn on savings, accounting for compound interest. Unlike the advertised interest rate, APY shows your actual earnings after all the compounding magic happens. This comprehensive guide teaches you the APY formula, shows real calculation examples, and explains why APY is the only number that matters when choosing where to park your money.

What is APY? The Complete Definition

APY (Annual Percentage Yield) is the effective annual rate of return earned on an interest-bearing account, taking into account the effect of compounding interest.

The key difference:

• Interest Rate (APR): The simple annual rate before compounding
• APY: The actual annual return after compounding

Why APY is Always Higher Than the Interest Rate

Example: 5.0% interest rate, compounded daily

• Stated rate: 5.0%
• Actual APY: 5.127%
• The 0.127% difference comes from compound interest (earning interest on your interest)

Key insight: The more frequently interest compounds, the bigger the gap between the stated rate and APY.

Compounding frequency impact on 5% rate:

| Compounding | APY | |-------------|-----| | Annually | 5.000% | | Quarterly | 5.095% | | Monthly | 5.116% | | Daily | 5.127% | | Continuously | 5.127% |

The magic: Daily compounding on a 5% rate produces the same return as 5.127% simple interest – you earn an extra $12.70 per year on every $10,000.

The APY Formula Explained

The standard APY formula is:

APY = (1 + r/n)^n - 1

Where:

• r = Annual interest rate (as decimal: 5% = 0.05)
• n = Number of compounding periods per year
• ^ = Exponent (raised to the power of)

Breaking Down Each Component

r/n: Interest rate per compounding period

• Annual rate 5% (0.05) compounded monthly: 0.05/12 = 0.004167 per month

(1 + r/n): Growth factor per period

• 1.004167 = You have 100.4167% of your money after each month

(1 + r/n)^n: Growth over full year

• 1.004167^12 = 1.0511619 = You have 105.116% after 12 months

Subtract 1: Convert to percentage earned

• 1.0511619 - 1 = 0.0511619 = 5.116% APY

Different Compounding Frequencies

n values for different compounding schedules:

• Annual: n = 1
• Semi-annual: n = 2
• Quarterly: n = 4
• Monthly: n = 12
• Weekly: n = 52
• Daily: n = 365
• Continuous: Different formula (e^r - 1)

Step-by-Step APY Calculation Examples

Example 1: Basic APY Calculation (Monthly Compounding)

Scenario: Savings account with 4.5% interest, compounded monthly. What's the APY?

Given:

• r = 4.5% = 0.045
• n = 12 (monthly)

Step 1: Divide rate by compounding periods

• r/n = 0.045 / 12 = 0.00375

Step 2: Add 1

• 1 + 0.00375 = 1.00375

Step 3: Raise to the power of n

• 1.00375^12 = 1.0459318

Step 4: Subtract 1

• 1.0459318 - 1 = 0.0459318

Step 5: Convert to percentage

• 0.0459318 × 100 = 4.593% APY

What this means: A 4.5% rate compounded monthly produces the same return as a 4.593% simple annual rate. You earn an extra 0.093% due to compounding.

On $10,000: That's an extra $9.30 per year from compounding alone.

Example 2: Daily Compounding Calculation

Scenario: High-yield savings account advertises 5.25% interest, compounded daily. Calculate APY.

Given:

• r = 5.25% = 0.0525
• n = 365 (daily)

Calculation:

• APY = (1 + 0.0525/365)^365 - 1
• APY = (1 + 0.00014384)^365 - 1
• APY = (1.00014384)^365 - 1
• APY = 1.053872 - 1
• APY = 0.053872
• APY = 5.387%

Impact: The 0.137% boost from daily compounding earns you $13.70 extra per year on $10,000.

This is why APY matters: Two banks might both advertise "5.25% interest," but if one compounds monthly (5.367% APY) and one compounds daily (5.387% APY), the daily compounding bank pays $2 more per $10,000.

Example 3: Quarterly Compounding Calculation

Scenario: CD (Certificate of Deposit) offers 4.0% APR, compounded quarterly.

Given:

• r = 4.0% = 0.04
• n = 4 (quarterly)

Calculation:

• APY = (1 + 0.04/4)^4 - 1
• APY = (1 + 0.01)^4 - 1
• APY = (1.01)^4 - 1
• APY = 1.04060401 - 1
• APY = 4.060%

On a $20,000 CD:

• Simple 4% would earn: $800
• Actual earnings with compounding: $812
• Extra from compounding: $12

Example 4: Comparing Two Accounts

Which account earns more?

Account A:

• Rate: 5.15%
• Compounding: Monthly
• APY = (1 + 0.0515/12)^12 - 1 = 5.274%

Account B:

• Rate: 5.10%
• Compounding: Daily
• APY = (1 + 0.051/365)^365 - 1 = 5.230%

Winner: Account A (5.274% APY) despite having only 0.05% higher rate, because monthly vs daily doesn't matter as much when you're already at a higher base rate.

On $30,000:

• Account A earns: $1,582.20
• Account B earns: $1,569.00
• Difference: $13.20/year

Example 5: Reverse Engineering – Finding the Rate

Scenario: Bank advertises 5.15% APY with daily compounding. What's the underlying interest rate?

Given:

• APY = 5.15% = 0.0515
• n = 365

Reverse formula: r = n × [(1 + APY)^(1/n) - 1]

Calculation:

• r = 365 × [(1.0515)^(1/365) - 1]
• r = 365 × [1.000136986 - 1]
• r = 365 × 0.000136986
• r = 0.05 = 5.0%

Answer: The underlying interest rate is exactly 5.0%.

Why this matters: If you're comparing accounts and one shows only APY while another shows only the rate, you can convert between them to compare apples-to-apples.

Real-World APY Scenarios

Scenario 1: High-Yield Savings Account

Your situation: You have $25,000 emergency fund to park in a HYSA.

Account options:

• Marcus by Goldman Sachs: 5.00% APY (daily compounding)
• Ally Bank: 4.85% APY (daily compounding)
• Local Credit Union: 4.25% APY (monthly compounding)

Annual earnings:

• Marcus: $25,000 × 0.05 = $1,250
• Ally: $25,000 × 0.0485 = $1,212.50
• Credit Union: $25,000 × 0.0425 = $1,062.50

Difference: Choosing Marcus over credit union = $187.50 more per year for the same $25,000.

5-year impact (assuming rates hold):

• Marcus: $6,891 earned
• Credit Union: $5,846 earned
• Lost opportunity: $1,045 by choosing lower APY

Action: Use our APY Calculator to compare your actual account options.

Scenario 2: Certificate of Deposit (CD)

Your situation: $50,000 to invest in a 12-month CD.

CD options (all 12-month terms):

• Bank A: 5.25% APY
• Bank B: 5.20% APY
• Bank C: 5.15% APY

Earnings after 12 months:

• Bank A: $50,000 × 1.0525 = $52,625 ($2,625 interest)
• Bank B: $50,000 × 1.0520 = $52,600 ($2,600 interest)
• Bank C: $50,000 × 1.0515 = $52,575 ($2,575 interest)

Difference: 0.10% APY difference = $50 on $50,000 over 12 months.

Key insight: On CDs, even small APY differences add up. 0.10% seems tiny but it's $50 per $50K per year.

Scenario 3: Monthly Contributions with APY

Your situation: Contributing $500/month to savings earning 5.0% APY.

Year 1 calculation (complex because contributions happen monthly):

Month 1: $500 × 1.05^(11/12) = $522.20 Month 2: $500 × 1.05^(10/12) = $520.60 ... Month 12: $500 × 1.05^(0/12) = $500.00

Total after 12 months: $6,152

• Total contributed: $6,000
• Interest earned: $152

Important: When making regular contributions, you can't just multiply total contributions by APY because each contribution earns interest for different lengths of time.

Use our calculator: For contribution scenarios, you need a dedicated savings calculator that accounts for the timing of deposits.

Scenario 4: Compound Interest Over Multiple Years

Your situation: $10,000 initial deposit, 4.5% APY, no additional contributions.

Growth over time:

| Year | Beginning Balance | Interest Earned | Ending Balance | |------|------------------|-----------------|----------------| | 1 | $10,000 | $450.00 | $10,450.00 | | 2 | $10,450 | $470.25 | $10,920.25 | | 3 | $10,920.25 | $491.41 | $11,411.66 | | 5 | $12,461.82 | $560.78 | $13,022.60 | | 10 | $15,529.69 | $698.84 | $16,228.53 | | 20 | $24,117.14 | $1,085.27 | $25,202.41 |

Key observations:

• Year 1: Earned $450 (4.5% of $10K)
• Year 2: Earned $470 (4.5% of $10,450) – $20 more than Year 1
• Year 10: Earned $699 (4.5% of $15,530) – 55% more than Year 1
• By Year 20: Your interest earnings ($1,085) are more than double your Year 1 interest ($450)

This is compounding in action: The same 4.5% APY produces exponentially growing dollar amounts because the base keeps growing.

How to Calculate APY With a Calculator

Using a Standard Calculator

Problem: Calculate APY for 5.5% compounded monthly.

Button sequence:

1. Calculate r/n: 0.055 ÷ 12 = 0.0045833
2. Add 1: + 1 = 1.0045833
3. Raise to power: y^x or ^ button, enter 12, = → 1.0564167
4. Subtract 1: - 1 = 0.0564167
5. Convert to %: × 100 = 5.64%

Using Excel or Google Sheets

Formula in Excel/Sheets: Type =(1 + rate/n)^n - 1 where rate and n are replaced with your values.

Example:

• Type: =((1 + 0.055/12)^12 - 1)
• Result: 0.0564167
• Format as percentage: 5.64%

For multiple calculations, create a table:

• Column A: Interest Rate
• Column B: Compounding Frequency (n)
• Column C: Type the formula =(1+A2/B2)^B2-1
• Format Column C as percentage

Using Our APY Calculator

Our APY Calculator handles all the math instantly:

1. Enter interest rate: e.g., 5.5%
2. Select compounding frequency: Daily, Monthly, Quarterly, etc.
3. Enter initial deposit (optional): To see dollar growth
4. Add monthly contributions (optional): For ongoing savings
5. Click Calculate: See APY, total interest, year-by-year growth

Bonus features:

• Compare multiple accounts side-by-side
• Model contribution scenarios
• See amortization table of growth over time
• Download results as CSV

Why APY Matters More Than Interest Rate

Reason 1: Apples-to-Apples Comparison

The problem: Banks advertise rates differently.

• Bank A: "5.00% interest compounded daily"
• Bank B: "4.95% interest compounded monthly"
• Bank C: "5.10% APY"

Which is best? You can't tell without converting all to APY:

• Bank A: 5.127% APY ✓ Winner
• Bank B: 5.059% APY
• Bank C: 5.10% APY (need to reverse-engineer the rate to understand compounding)

With APY: Just compare the APY numbers directly. Higher APY = more money in your pocket.

Reason 2: Shows True Cost/Benefit

On savings: APY shows what you actually earn, accounting for compounding.

Example: $20,000 at 5% rate daily compounding

• If you think: 5% rate = $1,000/year
• Reality: 5.127% APY = $1,025/year
• You earn: $25 more than you expected

Reason 3: Required by Law for Transparency

Truth in Savings Act requires banks to disclose APY on savings accounts and CDs, precisely because consumers were confused by different compounding methods.

The law: APY must be displayed more prominently than the interest rate.

What to look for: When comparing accounts, always use APY as your comparison metric. Ignore the stated interest rate for comparison purposes (though it's still useful for understanding).

Reason 4: Accounts for Different Compounding Frequencies

Examples:

4.8% rate, various compounding:

• Daily: 4.917% APY
• Monthly: 4.898% APY
• Quarterly: 4.874% APY
• Annually: 4.8% APY (no compounding benefit)

Impact on $15,000:

• Daily: Earns $737.55
• Annually: Earns $720.00
• Difference: $17.55/year purely from compounding frequency

APY lets you see this difference at a glance, whereas comparing "4.8% daily" vs "4.8% annually" doesn't immediately reveal the $17.55 gap.

APY vs APR: What's the Difference?

APY (Annual Percentage Yield)

• Used for: Savings accounts, CDs, money market accounts
• Represents: What you earn
• Includes: Effect of compound interest
• Higher is better: You want high APY

APR (Annual Percentage Rate)

• Used for: Loans, mortgages, credit cards
• Represents: What you pay
• Includes: Interest + fees
• Lower is better: You want low APR

The Compounding Difference

APY: Includes effect of compounding (earning interest on interest) → APY > interest rate

APR: Does NOT include effect of compounding → APR = interest rate + fees, but not adjusted for compounding

Example:

• Savings account: 5% rate → 5.127% APY (compounding helps you)
• Credit card: 20% rate → 20% APR (compounding hurts you, but APR doesn't show it)

Caution: Credit cards with 20% APR actually cost you MORE than 20% if you carry a balance, because interest compounds. The effective rate you pay can be 21-22%+ due to daily compounding of unpaid interest.

Common APY Calculation Mistakes

Mistake 1: Using APY for Multi-Year Projections

The error: $10,000 at 5% APY for 3 years = $10,000 × 1.05 × 1.05 × 1.05 = $11,576

Why it's wrong: You're compounding the APY, but APY already includes one year of compounding.

Correct method: Use the underlying rate with proper compounding.

• $10,000 × (1 + 0.05/365)^(365×3) = $11,618

Or: Use 5% simple rate: $10,000 × 1.05^3 = $11,576 (this happens to equal the wrong method above, but only because daily compounding ≈ continuous compounding)

The fix: For multi-year calculations, use our Compound Interest Calculator which properly handles compounding over multiple years.

Mistake 2: Ignoring Fees

The error: Choosing highest APY without considering fees.

Example:

• Account A: 5.25% APY, $10/month fee if balance under $25K
• Account B: 5.00% APY, no fees

Your situation: $15,000 balance

Actual returns:

• Account A: $787.50 interest - $120 fees = $667.50 net
• Account B: $750 interest - $0 fees = $750 net

Winner: Account B, despite lower APY.

The fix: Calculate net APY after fees.

• Account A net: ($667.50 / $15,000) = 4.45% net APY
• Account B net: 5.00% APY (no fees)

Mistake 3: Not Accounting for Taxes

The error: Calculating returns without considering that interest is taxable.

Example: $30,000 at 5% APY = $1,500 interest

• If you think: I made $1,500
• Reality (24% tax bracket): I made $1,500 - $360 tax = $1,140 after-tax

After-tax APY: $1,140 / $30,000 = 3.8% after-tax APY

The fix: For high earners, consider after-tax returns:

• Tax-free muni bonds: Lower rate but no federal tax
• I Bonds: Deferred tax until maturity
• Roth IRA: Contributions grow tax-free

Use our I Bond or Tax Calculator to compare after-tax returns.

Mistake 4: Assuming APY is Fixed

The error: Planning future savings assuming today's 5% APY will last forever.

Reality: APY on savings accounts is variable and changes with Fed interest rates.

Example: 2020-2021 APY was 0.5%, then rose to 5%+ by 2023, and may drop again in future years.

The fix:

• For guaranteed returns, use CDs (fixed APY for term)
• For savings accounts, expect APY to vary
• Plan conservatively (use 3% in calculations even if current rate is 5%)

Mistake 5: Confusing APY With Absolute Returns

The error: "5% APY is always 5% APY."

Truth: Same APY produces different dollar amounts depending on balance.

Example: 5% APY on:

• $1,000 balance: $50/year
• $10,000 balance: $500/year
• $100,000 balance: $5,000/year

Why it matters: Focusing on APY alone without considering the balance can lead to poor decisions.

Example decision:

• Move $2,000 from 4% to 5% APY: Gain $20/year
• Move $50,000 from 4.9% to 5% APY: Gain $50/year

The $50K move is worth more of your time even though the APY difference is smaller (0.1% vs 1%), because the balance is larger.

How APY Changes Your Savings Strategy

Strategy 1: Chase the Highest APY (With Limits)

Approach: Move money to highest APY account as rates change.

Example:

• Current account: 4.5% APY
• New account: 5.3% APY
• Balance: $40,000
• Annual gain: $320

Worth it if:

• Account transfer takes less than 2 hours of time ($160/hr effective wage)
• No transfer fees
• No minimum balance penalties on old account

Not worth it if:

• Difference is less than 0.25% APY (only $100/year on $40K)
• New account has fees, minimums, or hoops to jump through
• You have to transfer again in 3 months when rates change

Our take: Chase high APY, but don't let it consume your life. Set a threshold (e.g., "I'll move money for 0.50%+ APY improvement") and stick to it.

Strategy 2: Ladder CDs for Higher Average APY

The problem: Regular savings accounts have variable APY; CDs lock you in.

The solution: CD ladder

Example: $25,000 to invest

• $5,000 in 1-year CD at 4.5% APY
• $5,000 in 2-year CD at 4.7% APY
• $5,000 in 3-year CD at 4.9% APY
• $5,000 in 4-year CD at 5.0% APY
• $5,000 in 5-year CD at 5.1% APY

What happens:

• Year 1: First CD matures → Reinvest in new 5-year CD
• Year 2: Second CD matures → Reinvest in new 5-year CD
• After 5 years: One CD matures every year

Benefits:

• Higher average APY than savings account (4.84% vs 4.5%)
• Access to cash every year (liquidity)
• Protected from rate drops (CDs are locked in)

Use our CD Calculator to model ladder scenarios.

Strategy 3: Combine High APY Savings + Investment

The reality: Even 5% APY savings severely underperforms stocks long-term (10% average).

The strategy:

• Emergency fund (3-6 months expenses): High APY savings (5%+)
• Short-term savings (house down payment in 1-2 years): High APY savings or CDs
• Long-term savings (retirement, 10+ years): Invest in stock market (index funds)

Example: $60,000 to allocate

• $15,000 emergency fund → HYSA at 5% = $750/year
• $20,000 house fund (need in 2 years) → 2-year CD at 4.8% = $960/year
• $25,000 retirement savings → S&P 500 index (10% avg) = $2,500/year
• Total return: $4,210/year (7% average)

If you put all $60K in 5% savings: $3,000/year

Opportunity cost: $1,210/year by not investing appropriately.

The fix: Use APY for cash you need in under 3 years. Use investment returns for money you don't need for 5+ years.

Frequently Asked Questions

Q: Is APY really guaranteed?

A: For CDs and fixed-rate accounts, yes, the APY is guaranteed for the term. For regular savings accounts and HYSAs, APY is variable and can change anytime (usually follows Fed rate changes). Check if the account is fixed or variable APY.

Q: Why does my bank statement show different interest than the APY suggests?

A: Probably because: (1) You made deposits/withdrawals mid-month (interest calculated on daily balance), (2) Bank changed APY during the month, (3) Fees were deducted, or (4) You're looking at a partial month. APY assumes you hold the same balance for a full year with no changes.

Q: Can APY be negative?

A: In theory yes (if banks charged you to hold deposits), but in practice, U.S. banks don't have negative APY. The Fed's key rate would have to go significantly negative first. Some European banks had negative rates in 2010s, but not common in the U.S.

Q: What's a good APY in 2026?

A: As of early 2026, good APY for savings:

• Excellent: 5.0%+ (top online banks)
• Good: 4.5-5.0% (competitive online banks)
• Fair: 4.0-4.5% (some credit unions, smaller banks)
• Poor: Under 1.0% (big national banks like Chase, BofA often pay this)

For CDs, add 0.25-0.75% to the above for longer terms (3-5 years).

Q: Does APY include bank bonuses?

A: No. APY only reflects interest earned on your deposits. Sign-up bonuses ($200 for opening account) are separate and not included in APY calculations. However, if you account for the bonus, your effective first-year return is higher.

Example: Deposit $10,000, earn 5% APY ($500) + $200 bonus = $700 total = 7% effective return in year 1.

Q: Why do some accounts advertise "up to 5% APY"?

A: Tiered APY: Different APY based on balance tiers.

Example:

• $0-$5,000: 0.50% APY
• $5,001-$25,000: 3.00% APY
• $25,001+: 5.00% APY

If you have $30,000: You DON'T earn 5% on all of it. You earn 0.5% on first $5K, 3% on next $20K, 5% on remaining $5K. This is called a blended APY.

The fix: Read the fine print on tiered rates. Sometimes "up to 5%" means only a tiny portion of your balance earns that rate.

Conclusion: APY is Your True Return Metric

Calculating APY isn't just an academic exercise – it's the only way to know what you're really earning on your savings. The advertised interest rate can be manipulated with different compounding frequencies, but APY cuts through the marketing noise to show your true annual return.

Your action plan:

1. Always compare accounts by APY, not interest rate
2. Use our calculator to compute APY for any rate/compounding combo
3. Chase high APY but only when the difference is meaningful (0.5%+)
4. Check APY regularly (savings account rates change with Fed policy)
5. Calculate after-tax APY if you're in a high tax bracket
6. Combine high APY savings with investments for balanced strategy

Remember: A 5% APY savings account is risk-free and guaranteed (up to FDIC limits). That's powerful in a world of volatile investments. Max out your emergency fund and short-term savings in the highest APY account you can find, then invest the rest for long-term growth.

Ready to calculate your earnings? Use our APY Calculator now to see exact dollar amounts.

Related calculators:

• Compound Interest Calculator – See growth over multiple years
• Savings Goal Calculator – How much to save monthly
• CD Calculator – Compare CD terms and rates