Compound vs Simple Interest
Growth Over Time
Year-by-Year Growth
| Year | Balance at Start | Interest Earned | Contributions | Balance at End |
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How to Use This Calculator
Enter your starting amount, the interest rate, and how many years you're investing for. Pick how often the interest compounds - daily gives you slightly more than monthly or annual compounding.
If you plan to add money regularly, select your contribution frequency and amount. The calculator shows how compounding compares to simple interest, with a chart and yearly breakdown of your balance growth.
Understanding Compound Interest
What Is Compound Interest?
It's interest earned on both your initial deposit and previously earned interest. You earn interest on your principal, that interest gets added to your balance, and you earn interest on the new total.
Your balance grows faster each year. The concept explains why savings accounts with higher rates and more frequent compounding earn more money.
Simple interest works differently. If you deposit $5,000 at 8%, simple interest earns $400 every year, totaling $9,000 after 10 years. Compounding grows the same deposit to $10,794 - an extra $1,794. Over 30 years, simple interest yields $17,000 while compounding yields $50,313.
The Rule of 72
Divide 72 by your interest rate to estimate doubling time. At 8%, money doubles in roughly 9 years (72÷8=9). At 6%, it takes 12 years. At 12%, only 6 years. A 1-2% rate difference can mean thousands or tens of thousands of dollars over 20-30 years.
Frequency and Time
How often interest compounds affects returns. Over 10 years at 6%, $25,000 with annual compounding becomes $44,771 while daily compounding yields $45,473 - a $702 difference.
At 8%, $5,000 grows to $5,832 in 2 years, $10,794 in 10 years, and $23,305 in 20 years. The second decade earns over twice what the first decade earned. Each year of compounding matters - you can't make up for lost time.
Regular Contributions
Regular deposits increase returns. If you start with $5,000 and add $100 monthly at 8%, you'll have $22,552 after 10 years instead of $10,794.
Your $17,000 invested ($5,000 initial + $12,000 added) produces $5,552 in interest.
Getting the Most from Compounding
- Ten extra years of compounding from age 25-35 often beats doubling your yearly deposits from 35-65
- Early withdrawals cost more than just the amount you take out - you lose all future compound growth on that money
- On $100,000, the difference between 0.01% and 4.5% APY is $4,490 annually
- Reinvested dividends and interest compound along with your principal
- Tax-advantaged accounts like 401(k)s and IRAs let your money compound without annual tax drag
- Credit card debt at 20-30% APR compounds against you, often doubling balances in 2-3 years
- Daily compounding beats monthly or annual when rates are equal
Compounding Frequency
Annual compounding calculates interest once per year. Put $1,000 into an account at 8% and you have $1,080 after year 1, then earn 8% on $1,080 in year 2. Monthly compounding divides the rate by 12 and compounds each month - interest earned in January starts earning interest in February. Some bonds use annual while most savings accounts and credit cards use monthly compounding.
Daily
Interest compounds every day based on your daily balance. Most high-yield savings accounts offer this.
Continuous
A mathematical concept where interest compounds infinitely often, representing the theoretical maximum for any rate. Few banks offer continuous compounding for retail accounts. With $1,000 at 8% for 10 years, continuous yields $2,226 versus $2,220 for daily - only $6 more.
Over 30 years with $100,000 at 6%, annual compounding yields $574,349 while daily yields $602,257. With $500,000, the compounding frequency difference could be $50,000 over 30 years.
Common Examples
Bank Accounts
High-yield savings accounts typically offer 4-5% APY with daily compounding. On $50,000 at 4.5%, daily compounding earns $2,300 annually versus $2,265 with annual compounding.
Most CDs use monthly or quarterly compounding with guaranteed rates. A 5-year CD at 5% with monthly compounding turns $10,000 into $12,833. Early withdrawal penalties can negate interest earned.
Investment Returns
Stock returns compound through reinvested dividends and capital gains. The S&P 500's 10% average annual return compounds $25,000 to $168,187 in 20 years when dividends are reinvested.
Retirement Accounts
401(k)s and IRAs grow tax-free or tax-deferred. Investing $500/month from age 25-65 at 8% yields $1.75 million. Starting at 35 instead yields only $745,000.
Debt
A $3,000 credit card balance at 22% APR compounds monthly. With minimum payments, most of your money goes to interest rather than principal.
A $300,000 mortgage at 6% over 30 years costs $347,000 in interest. Extra principal payments reduce this total by interrupting compounding.
The Compound Interest Formula
Basic Compound Interest Formula
Where:
A = Final amount
P = Principal (starting amount)
r = Annual interest rate (as decimal, so 8% = 0.08)
n = Compounding frequency per year (monthly = 12, daily = 365)
t = Time in years
Example: With $2,000 at 7% for 10 years, compounded monthly
A = 2,000(1 + 0.07/12)^(12×10)
A = 2,000(1.00583)^120
A = $4,019
With Regular Contributions
This formula combines the compound growth of your initial deposit with the compound growth of each regular contribution.
Effective Annual Rate (APY)
APY shows what you actually earn in a year including compounding effects. APR is the base rate without accounting for how often interest compounds. An 8% rate compounded monthly has an APY of 8.3%, while daily compounding yields 8.33%.
Continuous Compounding Formula
Where e = 2.71828 (Euler's number)
This is the theoretical maximum growth. The difference between daily and continuous compounding is negligible for practical purposes.
Practical Examples
Starting Early
Investor A starts at 25, invests $5,000 annually for 10 years, then stops - total contributed is $50,000. Investor B starts at 35, invests $5,000 annually for 30 years - total contributed is $150,000. At 65 with 8% returns, A has $787,000 while B has $611,000. A invests $100,000 less but finishes with $176,000 more.
With $50,000 invested at age 25 at 9%, you'd have $1.03 million by 65. Investing the same amount at age 35 yields $435,000 by 65 - about $600,000 less.
Long-Term Saving and Debt
Investing $500 monthly from age 30 to 65 at 8% yields $1.13 million. Your contributions total $210,000 while interest accounts for $920,000 - about 81% of the final balance.
On the debt side, a $7,500 credit card balance at 23% APR means most of your minimum payments go toward interest rather than reducing what you owe.
Important Notes
This calculator provides estimates for educational purposes only. Actual returns will vary based on market conditions, fees, taxes, and other factors. Past performance doesn't guarantee future results. This is not financial advice. Consider consulting a financial advisor for personalized guidance.