Last Updated: February 2026 • 28 min read
Daily Compound Interest: The Complete Guide
Daily compound interest calculates and adds interest to your balance every single day, allowing you to earn interest on your interest 365 times per year. This results in faster growth compared to monthly, quarterly, or annual compounding. This guide explains exactly how daily compounding works, where to find it, and how much more you can earn. Use our compound interest calculator to see how daily compounding can grow your money.
- Daily compounding calculates interest 365 times per year, earning interest on interest every day
- $10,000 at 5% for 10 years grows to $16,486.65 with daily compounding vs. $16,288.95 with annual
- High-yield savings accounts and many CDs use daily compounding
- The daily rate is your annual rate divided by 365 (e.g., 5% / 365 = 0.0137% per day)
- Use our compound interest calculator to compare daily vs. other compounding frequencies
- Credit cards also use daily compounding, which is why debt grows so quickly
What Is Daily Compound Interest?
Daily compound interest means your financial institution calculates interest on your balance once every day. Each day, the interest earned is added to your principal, so the next day you earn interest on a slightly larger balance. Over time, this daily cycle creates an accelerating growth pattern.
The key difference from other compounding frequencies is how often the interest is calculated and added:
- Annual compounding: Interest is calculated and added once per year
- Quarterly compounding: Interest is calculated and added 4 times per year
- Monthly compounding: Interest is calculated and added 12 times per year
- Daily compounding: Interest is calculated and added 365 times per year
With daily compounding, your money starts earning interest on its interest after just one day, rather than waiting a month or a year. While the difference on any single day is tiny, over months and years it adds up meaningfully. According to the SEC's Guide to Savings and Investing, understanding compounding is one of the most important concepts for building long-term wealth.
How Daily Compounding Works Mathematically
Understanding the mathematics behind daily compounding helps you appreciate why this frequency creates superior returns over time. The core concept is simple: each day, a tiny amount of interest is added to your balance, and the next day's interest calculation uses this new, slightly larger balance.
Think of daily compounding as a 365-step staircase rather than a single annual jump. Each step is small, but because you're always climbing from the previous step's height, you end up higher than if you took one big leap at the end of the year.
The Mathematical Progression
Here's how your balance grows day by day with daily compounding at 5% APR on $10,000:
Day 1: $10,000.00 + ($10,000.00 x 0.05/365) = $10,001.37
Day 2: $10,001.37 + ($10,001.37 x 0.05/365) = $10,002.74
Day 30: $10,041.10
Day 90: $10,124.11
Day 180: $10,249.49
Day 365: $10,512.67
The key insight is that each day's interest calculation includes all previously earned interest. By day 365, your daily interest is $1.44 instead of the initial $1.37 because you're now earning interest on $10,499+ rather than $10,000. This mathematical reality is why daily compounding produces the characteristic exponential growth curve that makes compound interest so powerful for long-term wealth building.
The SEC's compound interest calculator uses similar mathematics to help investors understand how their money can grow over time.
The Daily Compound Interest Formula
The formula for daily compound interest is the standard compound interest formula with n = 365:
Where:
- A = Final amount (principal + interest)
- P = Principal (initial deposit or investment)
- r = Annual interest rate (as a decimal, so 5% = 0.05)
- 365 = Number of compounding periods per year (days)
- t = Time in years
Step-by-Step Calculation Example
Let's calculate what $5,000 deposited at 4.5% APR with daily compounding earns after 3 years:
A = $5,000 x (1.00012329)1,095
A = $5,000 x 1.14408
A = $5,720.42
After 3 years, your $5,000 earns $720.42 in interest with daily compounding. With annual compounding at the same rate, you'd earn $705.42 — so daily compounding earns you an additional $15.00.
Which Accounts Use Daily Compounding
Daily compounding is more common than many people realize. The Consumer Financial Protection Bureau (CFPB) recommends understanding how your accounts compound interest when comparing financial products. Here's a comprehensive breakdown of which account types typically use daily compounding:
Accounts with Daily Compounding (Works FOR You)
| Account Type | Compounding | Typical APY Range | Notes |
|---|---|---|---|
| High-Yield Savings | Daily | 4.00% - 5.25% | Most online banks compound daily, pay monthly |
| Money Market Accounts | Daily | 3.75% - 5.10% | Higher minimums, check-writing privileges |
| CDs (Most) | Daily | 4.00% - 5.50% | Verify before opening; some compound monthly |
| Treasury I Bonds | Semi-annually | Variable | Government-backed, inflation-adjusted |
| Traditional Savings | Monthly/Quarterly | 0.01% - 0.50% | Brick-and-mortar banks often compound less frequently |
Accounts with Daily Compounding (Works AGAINST You)
| Debt Type | Compounding | Typical APR Range | Impact |
|---|---|---|---|
| Credit Cards | Daily | 18.99% - 29.99% | Most expensive consumer debt |
| Private Student Loans | Daily or Monthly | 4.99% - 14.99% | Varies by lender |
| Federal Student Loans | Daily | 5.50% - 8.05% | Interest accrues from disbursement |
| Personal Loans | Monthly | 6.99% - 35.99% | Usually simple interest |
| Mortgages | Monthly | 6.00% - 8.00% | Amortized, not compound |
The FDIC insures deposits at member banks up to $250,000 per depositor, per insured bank. This protection applies regardless of compounding frequency, making high-yield savings accounts with daily compounding a safe and effective way to grow your emergency fund.
Daily vs. Other Compounding Frequencies
How much does daily compounding actually matter? This compounding frequency comparison shows the differences using $10,000 at 5% APR over different time periods:
5-Year Comparison
| Frequency | n Value | Final Amount | Interest Earned | Difference from Annual |
|---|---|---|---|---|
| Annually | 1 | $12,762.82 | $2,762.82 | — |
| Semi-annually | 2 | $12,800.85 | $2,800.85 | +$38.03 |
| Quarterly | 4 | $12,820.37 | $2,820.37 | +$57.55 |
| Monthly | 12 | $12,833.59 | $2,833.59 | +$70.77 |
| Daily | 365 | $12,840.03 | $2,840.03 | +$77.21 |
10-Year Comparison
| Frequency | n Value | Final Amount | Interest Earned | Difference from Annual |
|---|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 | — |
| Semi-annually | 2 | $16,386.16 | $6,386.16 | +$97.21 |
| Quarterly | 4 | $16,436.19 | $6,436.19 | +$147.24 |
| Monthly | 12 | $16,470.09 | $6,470.09 | +$181.14 |
| Daily | 365 | $16,486.65 | $6,486.65 | +$197.70 |
30-Year Comparison
| Frequency | n Value | Final Amount | Interest Earned | Difference from Annual |
|---|---|---|---|---|
| Annually | 1 | $43,219.42 | $33,219.42 | — |
| Semi-annually | 2 | $44,012.44 | $34,012.44 | +$793.02 |
| Quarterly | 4 | $44,420.21 | $34,420.21 | +$1,200.79 |
| Monthly | 12 | $44,677.44 | $34,677.44 | +$1,458.02 |
| Daily | 365 | $44,812.30 | $34,812.30 | +$1,592.88 |
Key observations:
- Over 5 years, daily compounding earns $77 more than annual — modest but meaningful
- Over 10 years, the gap widens to nearly $198
- Over 30 years, daily compounding earns $1,593 more than annual compounding on just $10,000
- The jump from monthly to daily is relatively small — most of the benefit comes from moving to at least monthly compounding
The APY Advantage of Daily Compounding
When comparing accounts, the APY (Annual Percentage Yield) tells you the true return after accounting for compounding. Daily compounding produces a higher APY than less frequent compounding at the same stated APR. This is why the Truth in Savings Act requires banks to disclose APY, ensuring consumers can make accurate comparisons.
How Daily Compounding Boosts Your APY
The difference between APR and APY reveals the "hidden" bonus from compounding. Here's how different compounding frequencies affect your effective yield:
| Stated APR | APY (Annual) | APY (Quarterly) | APY (Monthly) | APY (Daily) | Daily Boost |
|---|---|---|---|---|---|
| 3.00% | 3.000% | 3.034% | 3.042% | 3.045% | +0.045% |
| 4.00% | 4.000% | 4.060% | 4.074% | 4.081% | +0.081% |
| 5.00% | 5.000% | 5.095% | 5.116% | 5.127% | +0.127% |
| 6.00% | 6.000% | 6.136% | 6.168% | 6.183% | +0.183% |
| 7.00% | 7.000% | 7.186% | 7.229% | 7.250% | +0.250% |
At 5% APR, daily compounding gives you an effective APY of 5.127%, meaning you earn an extra 0.127% annually compared to annual compounding. On a $50,000 balance, that translates to an extra $63.50 per year in "free money" just from the compounding frequency.
Why This Matters for Account Shopping
When comparing savings accounts or CDs, always compare APY to APY, not APR to APR. An account advertising 4.90% APR with daily compounding actually yields 5.02% APY, while an account at 5.00% APR with annual compounding yields exactly 5.00% APY. The seemingly lower rate actually pays more.
Real-World Examples of Daily Compounding
Understanding daily compounding becomes more tangible with practical examples. Let's explore how daily compounding affects real financial scenarios that you might encounter.
Example 1: Emergency Fund Growth
Sarah deposits $15,000 into a high-yield savings account earning 4.75% APY with daily compounding:
Year 2: $15,728.37 -> $16,492.04 (+$763.67)
Year 3: $16,492.04 -> $17,293.08 (+$801.04)
Year 4: $17,293.08 -> $18,133.66 (+$840.58)
Year 5: $18,133.66 -> $19,015.97 (+$882.31)
Total Interest Earned: $4,015.97
Example 2: CD Ladder Strategy
Michael creates a CD ladder with $50,000, splitting it across terms with daily compounding:
| CD Term | Amount | APY | Maturity Value | Interest Earned |
|---|---|---|---|---|
| 6-Month | $10,000 | 5.00% | $10,252.84 | $252.84 |
| 12-Month | $10,000 | 5.15% | $10,528.04 | $528.04 |
| 18-Month | $10,000 | 4.85% | $10,747.06 | $747.06 |
| 24-Month | $10,000 | 4.50% | $10,934.69 | $934.69 |
| 36-Month | $10,000 | 4.25% | $11,340.41 | $1,340.41 |
| Total | $53,803.04 | $3,803.04 | ||
Example 3: College Savings (529 Plan Alternative)
Parents saving $300/month for 18 years in a daily-compounding account at 4.5% APY:
Final Balance: $102,847.23
Interest Earned: $38,047.23 (59% of contributions)
These examples demonstrate why choosing accounts with daily compounding matters for long-term savings goals. Use our compound interest calculator to model your own scenarios.
The 365-Day vs. 360-Day Convention
Not all financial institutions use the same number of days in their daily compounding calculations. There are two common conventions:
365/365 Method (Actual/Actual)
Most consumer banks and savings accounts use a 365-day year (366 in leap years). This is the most straightforward method and the one used in our calculator. The daily rate is simply the annual rate divided by 365.
360/365 Method (Banker's Year)
Some commercial loans and certain financial products use a 360-day year for interest calculation purposes, but accrue interest for all 365 actual days. This results in slightly higher effective interest because:
5% / 360 = 0.01389% per day (vs. 0.01370% with /365)
When this higher daily rate is applied across all 365 actual days, borrowers pay slightly more interest. On a $10,000 loan at 5% for one year:
- 365/365 method: $512.67 interest
- 360/365 method: $519.44 interest
- Difference: $6.77 extra per year
Always check which convention your bank or lender uses, especially for larger balances where the difference becomes more significant. The CFPB's Ask CFPB tool can help you understand these lending practices.
Which Accounts Offer Daily Compounding?
Daily compounding is more common than you might think. Here's where you'll typically find it:
Accounts That Usually Compound Daily
Most online banks and high-yield savings accounts compound interest daily and pay it monthly. Most high-yield savings accounts are FDIC insured up to $250,000. This is the most common consumer product with daily compounding.
Many CDs compound daily, though some compound monthly or quarterly. Check the terms before opening a CD, as compounding frequency affects your effective yield.
Most money market accounts at banks compound interest daily. They typically offer higher rates than regular savings accounts with similar daily compounding benefits.
Credit card companies compound interest daily on your unpaid balance. This is why credit card debt grows so quickly — the same principle that helps savers works against borrowers.
Accounts That Usually Don't Compound Daily
- Traditional savings accounts: Often compound monthly or quarterly
- Bonds: Typically pay interest semi-annually
- Mortgages: Usually compound monthly
- Student loans: Federal loans compound daily, but many private loans compound monthly
Daily Compounding at Different Interest Rates
The impact of daily compounding becomes more significant at higher interest rates. Here's how $10,000 grows over 10 years with daily compounding at various rates:
| Annual Rate | Daily Rate | After 1 Year | After 5 Years | After 10 Years | After 20 Years |
|---|---|---|---|---|---|
| 2% | 0.00548% | $10,201.99 | $11,051.63 | $12,213.87 | $14,917.86 |
| 3% | 0.00822% | $10,304.53 | $11,618.22 | $13,498.32 | $18,220.47 |
| 4% | 0.01096% | $10,408.08 | $12,213.87 | $14,917.86 | $22,253.53 |
| 5% | 0.01370% | $10,512.67 | $12,840.03 | $16,486.65 | $27,179.10 |
| 6% | 0.01644% | $10,618.31 | $13,498.32 | $18,220.47 | $33,198.20 |
| 7% | 0.01918% | $10,725.03 | $14,190.40 | $20,137.26 | $40,551.17 |
| 8% | 0.02192% | $10,832.78 | $14,918.03 | $22,253.53 | $49,530.32 |
| 10% | 0.02740% | $11,051.56 | $16,486.08 | $27,179.10 | $73,870.32 |
At 10% with daily compounding, your money nearly triples in just 10 years and grows to more than 7x in 20 years. You can track current savings rates influenced by the Federal Reserve's federal funds rate. This demonstrates why both the interest rate and compounding frequency matter significantly for long-term growth. For more on how interest accumulates in savings products, read our savings account interest guide.
Daily Compounding with Larger Balances
The dollar advantage of daily over annual compounding scales with your balance. Here's the comparison at 5% over 10 years:
| Initial Deposit | Daily Compounding | Annual Compounding | Extra Earned (Daily) |
|---|---|---|---|
| $1,000 | $1,648.67 | $1,628.89 | $19.78 |
| $5,000 | $8,243.33 | $8,144.47 | $98.86 |
| $10,000 | $16,486.65 | $16,288.95 | $197.70 |
| $25,000 | $41,216.63 | $40,722.37 | $494.26 |
| $50,000 | $82,433.25 | $81,444.73 | $988.52 |
| $100,000 | $164,866.51 | $162,889.46 | $1,977.05 |
| $500,000 | $824,332.54 | $814,447.31 | $9,885.23 |
| $1,000,000 | $1,648,665.07 | $1,628,894.63 | $19,770.44 |
With a $100,000 balance, daily compounding earns you nearly $2,000 more over 10 years compared to annual compounding. At $1 million, the difference exceeds $19,770. For institutional investors and large depositors, this difference is substantial.
How Credit Cards Use Daily Compounding Against You
While daily compounding is great for savers, credit card companies use the same principle to charge you more interest on unpaid balances. The CFPB's credit card resources explain how to manage credit card debt effectively. Here's how it works:
The Daily Periodic Rate (DPR)
Credit card companies divide your APR by 365 to get the Daily Periodic Rate. They then apply this rate to your outstanding balance every single day.
Daily Periodic Rate: 24.99% / 365 = 0.0685% per day
Balance: $5,000
Day 1 interest: $5,000 x 0.000685 = $3.42
Day 2 balance: $5,003.42 -> interest: $3.43
Day 3 balance: $5,006.85 -> interest: $3.43
Over one month (30 days) with no payments, a $5,000 balance at 24.99% APR accrues approximately $103.62 in interest. Over a full year with no payments, the balance grows to $6,415.49 — that's $1,415.49 in interest, which is more than the simple interest of $1,249.50 because of daily compounding.
Credit Card Compounding Cost Comparison
| Starting Balance | APR | After 1 Year (no payments) | Interest Charged |
|---|---|---|---|
| $2,000 | 19.99% | $2,442.22 | $442.22 |
| $5,000 | 22.99% | $6,289.55 | $1,289.55 |
| $5,000 | 24.99% | $6,415.49 | $1,415.49 |
| $10,000 | 24.99% | $12,830.97 | $2,830.97 |
| $15,000 | 29.99% | $20,244.01 | $5,244.01 |
This is why paying off credit card balances as quickly as possible is so important — daily compounding works powerfully against you at high interest rates.
How Purchases and Payments Interact with Daily Compounding
Credit card daily compounding becomes even more complex when you consider the timing of purchases and payments:
| Scenario | Starting Balance | Action | Monthly Interest Impact |
|---|---|---|---|
| Pay beginning of cycle | $5,000 | Pay $1,000 on day 1 | ~$79.42 (on avg $4,000) |
| Pay end of cycle | $5,000 | Pay $1,000 on day 30 | ~$101.23 (on avg $4,967) |
| New purchase early | $5,000 | Spend $500 on day 5 | ~$110.89 (on avg $5,417) |
| New purchase late | $5,000 | Spend $500 on day 25 | ~$104.45 (on avg $5,083) |
The timing of payments and purchases matters significantly with daily compounding. Paying early in your billing cycle reduces your average daily balance, resulting in less interest charged.
Daily Compounding with Regular Contributions
The real power of daily compounding shines when combined with regular deposits. Here's what happens when you start with $10,000 and add $500 per month at 5% with daily compounding:
| Year | Total Contributed | Balance (Daily) | Interest Earned |
|---|---|---|---|
| 1 | $16,000 | $16,657.12 | $657.12 |
| 3 | $28,000 | $30,391.54 | $2,391.54 |
| 5 | $40,000 | $46,021.37 | $6,021.37 |
| 10 | $70,000 | $93,951.63 | $23,951.63 |
| 15 | $100,000 | $153,393.87 | $53,393.87 |
| 20 | $130,000 | $227,266.23 | $97,266.23 |
| 25 | $160,000 | $319,309.05 | $159,309.05 |
| 30 | $190,000 | $434,208.73 | $244,208.73 |
After 25 years, your interest earned ($159,309) actually exceeds your total contributions ($160,000). By year 30, you've earned $244,209 in compound interest on $190,000 in contributions — your money has earned more than you put in. Use our compound interest calculator to model your own contribution scenario.
How to Calculate Daily Interest Manually
If you want to calculate daily interest without a calculator, here's the step-by-step process:
Method 1: Full Formula
For a single lump sum with no additional deposits:
- Convert the annual rate to a decimal: 5% -> 0.05
- Divide by 365: 0.05 / 365 = 0.000136986
- Add 1: 1.000136986
- Raise to the power of total days: (1.000136986)365xyears
- Multiply by principal
Method 2: Day-by-Day Tracking
For understanding daily changes or tracking credit card interest:
- Calculate the daily rate: Annual Rate / 365
- Multiply your current balance by the daily rate to get today's interest
- Add today's interest to the balance
- Repeat for each day
Day 2: $10,001.37 x 0.000137 = $1.37 -> Balance: $10,002.74
Day 3: $10,002.74 x 0.000137 = $1.37 -> Balance: $10,004.11
...
Day 30: $10,039.73 x 0.000137 = $1.38 -> Balance: $10,041.10
Day 365: $10,498.73 x 0.000137 = $1.44 -> Balance: $10,512.67
Notice how the daily interest gradually increases from $1.37 on Day 1 to $1.44 on Day 365. This is the compounding effect in action — you earn slightly more each day because your balance grows.
APY and Daily Compounding
APY (Annual Percentage Yield) is the effective annual rate that accounts for compounding. Daily compounding is standard at most banks, as the Truth in Savings Act requires APY disclosure that accounts for compounding frequency. When a bank advertises a rate, they must disclose both the APR (nominal rate) and the APY (effective rate after compounding). With daily compounding, the APY is always slightly higher than the APR.
Converting APR to APY with Daily Compounding
| APR (Stated Rate) | APY (Daily Compounding) | APY (Monthly Compounding) | Daily Advantage |
|---|---|---|---|
| 1.00% | 1.0050% | 1.0046% | +0.0004% |
| 2.00% | 2.0201% | 2.0184% | +0.0017% |
| 3.00% | 3.0453% | 3.0416% | +0.0037% |
| 4.00% | 4.0808% | 4.0742% | +0.0066% |
| 5.00% | 5.1267% | 5.1162% | +0.0105% |
| 6.00% | 6.1831% | 6.1678% | +0.0153% |
| 8.00% | 8.3278% | 8.2999% | +0.0279% |
| 10.00% | 10.5156% | 10.4713% | +0.0443% |
The "daily advantage" column shows how much more APY you get from daily vs. monthly compounding. While the percentages look small, on large balances they translate to meaningful dollar amounts.
Daily Compounding vs. Continuous Compounding
Continuous compounding represents the theoretical maximum — compounding an infinite number of times per year. It uses the formula A = Pert. How close does daily compounding get to this theoretical limit?
| Rate | Daily (365x) | Continuous | Difference on $10,000 |
|---|---|---|---|
| 3% | $10,304.53 | $10,304.55 | $0.02 |
| 5% | $10,512.67 | $10,512.71 | $0.04 |
| 7% | $10,725.03 | $10,725.08 | $0.05 |
| 10% | $11,051.56 | $11,051.71 | $0.15 |
After one year on $10,000, the difference between daily and continuous compounding is just pennies. Daily compounding captures over 99.99% of the benefit of continuous compounding, which is why it's considered essentially equivalent in practical terms.
Strategies to Maximize Daily Compounding
When comparing savings accounts or CDs, prioritize those that compound daily. Check the APY rather than APR, as APY already reflects the compounding frequency.
With daily compounding, every day your money sits in the account earns interest. Deposit funds as early as possible rather than waiting until the end of the month.
Every dollar withdrawn stops compounding. Leave your money in the account as long as possible to maximize the compounding effect over time.
Credit cards compound daily at high rates. Prioritize paying off this debt before focusing on savings, since the interest working against you is likely much higher than what you earn.
Automate regular deposits to your daily-compounding savings account. Consistent contributions combined with daily compounding creates powerful long-term growth.
Common Misconceptions About Daily Compounding
- "Daily compounding means I get paid interest daily." Not necessarily. Most banks compound daily but pay (credit) interest monthly. Compounding frequency and payment frequency are different.
- "Daily compounding is always better than monthly." For the same APR, yes. But a monthly-compounding account at 5.5% APR beats a daily-compounding account at 5.0% APR. The rate matters more than the compounding frequency.
- "I should move money between accounts for better daily compounding." Moving money costs you compounding days during the transfer. Unless the rate difference is significant, frequent transfers can actually reduce your returns.
- "Daily compounding makes a huge difference." On consumer-level balances (under $100,000), the difference between daily and monthly compounding is relatively modest. The rate itself and your total balance matter far more.
Spreadsheet Formulas for Daily Compounding
You can calculate daily compound interest in Excel or Google Sheets:
| Calculation | Formula | Example |
|---|---|---|
| Future Value | =P*(1+rate/365)^(365*years) | =10000*(1+0.05/365)^(365*10) |
| Interest Earned | =P*(1+rate/365)^(365*years)-P | =10000*(1+0.05/365)^(365*10)-10000 |
| Daily Interest | =balance*(rate/365) | =10000*(0.05/365) |
| APY from APR | =(1+rate/365)^365-1 | =(1+0.05/365)^365-1 |
| Built-in FV | =FV(rate/365,365*years,0,-P) | =FV(0.05/365,3650,0,-10000) |
Frequently Asked Questions
Daily compounding means interest is calculated on your balance every single day (365 times per year) and added to your principal. This means you earn interest on yesterday's interest starting the very next day, creating a compounding cycle that accelerates your growth compared to less frequent compounding schedules. Most high-yield savings accounts and many CDs use daily compounding.
The difference is modest on typical consumer balances. For $10,000 at 5% over 10 years, daily compounding earns $16,486.65 while monthly earns $16,470.09 — a difference of just $16.56. However, at higher balances and rates, the gap widens. On $100,000 at 5% over 10 years, the difference is about $166. The compounding frequency matters less than the interest rate and your total balance.
No. While most high-yield savings accounts and many CDs compound daily, traditional savings accounts at brick-and-mortar banks may compound monthly or quarterly. The account's Truth in Savings disclosure will specify the compounding frequency. Always check the APY, which accounts for compounding frequency, for a true comparison between accounts. The FDIC regulates these disclosures for member banks.
For savers, more frequent compounding is always better (assuming the same APR). Daily compounding is better than monthly, which is better than quarterly, which is better than annual. However, continuous compounding is theoretically even better than daily, though the practical difference is negligible — often just pennies per $10,000 per year. For borrowers on loans, the opposite is true: less frequent compounding means you pay less interest.
Use the formula A = P(1 + r/365)^(365t), where P is your principal, r is the annual interest rate as a decimal, and t is the number of years. For example, $10,000 at 5% for 10 years: A = 10000 x (1 + 0.05/365)^(3650) = $16,486.65. You can also use our free compound interest calculator to run the calculation instantly.
It depends on the interest rate. At 5% APR, the first day's interest on $10,000 is $10,000 x (0.05/365) = $1.37. At 4% APR, it's $1.10 per day. At 3% APR, it's $0.82 per day. Remember that with daily compounding, each subsequent day earns slightly more than the previous day because the balance grows.
Credit card companies use daily compounding because it maximizes the interest they collect from cardholders who carry balances. At high APRs (often 20-30%), daily compounding significantly increases the total interest charged compared to monthly compounding. The CFPB requires clear disclosure of these terms. This is why financial advisors consistently recommend paying credit card balances in full each month.
In a savings account with daily compounding, your bank calculates interest every day and adds it to your balance. This means even a deposit made mid-month immediately starts earning interest. While the daily amounts are small, over years they add up meaningfully. A $10,000 deposit at 5% APY earns approximately $1.37 on the first day, with that amount growing slightly each subsequent day as your balance increases.
APR (Annual Percentage Rate) is the stated interest rate without accounting for compounding. APY (Annual Percentage Yield) is the effective rate after compounding is factored in. With daily compounding, APY is always slightly higher than APR. For example, a 5.00% APR with daily compounding equals a 5.127% APY. Banks are required to disclose APY so consumers can accurately compare products.
Yes, the Rule of 72 works with daily compounding and is actually slightly more accurate for daily than annual compounding. To estimate how long it takes your money to double, divide 72 by the APY (not APR). At 5% APY with daily compounding, your money doubles in approximately 72/5 = 14.4 years. The actual time is 13.86 years, so the Rule of 72 provides a good quick estimate. Use our calculator for precise calculations.
Calculate Your Daily Compound Interest