Compound Interest Calculator
Calculate compound interest on savings and investments. Daily, monthly, annual compounding. Free compound growth calculator shows future value.
Results
Conversion Summary
$1,000 Investment Growth (1 Year)
Conversion Formula
routput = noutput × [(1 + rinput/ninput)ninput/noutput - 1]
where r = rate, n = periods per year
Note: This calculator converts between different compound interest frequencies. APY (Annual Percentage Yield) represents the actual yearly return including compounding.
APR vs APY: APR (Annual Percentage Rate) is the simple interest rate, while APY includes the effect of compounding.
Continuous Compounding: Represents the mathematical limit of compound interest using Euler's constant (e ≈ 2.71828).
The Power of Compound Interest: Your Path to Wealth
Albert Einstein allegedly called compound interest "the eighth wonder of the world," adding that "those who understand it, earn it; those who don't, pay it." Whether he actually said this or not, the sentiment rings true—compound interest can either build your wealth exponentially or drain it through debt. Our compound interest calculator helps you understand and harness this powerful financial force.
Insira aqui imagem ['exponential growth chart showing difference between simple and compound interest over 30 years'] , ['Compound vs Simple Interest Growth Comparison']
Understanding the Interest Rate Converter
Banks and financial institutions often quote interest rates using different compounding frequencies, making direct comparisons nearly impossible. A 6% APR compounded monthly isn't the same as 6% APY compounded annually. This calculator instantly converts between any compounding frequencies, revealing the true cost or return of financial products.
Key Insight: The more frequently interest compounds, the higher the effective annual rate. Daily compounding at 5% yields 5.13% annually, while monthly compounding yields 5.12%.
Real Example: Comparing Savings Accounts
Let's help Marcus choose between three high-yield savings accounts with different terms:
Marcus's Savings Account Options
| Bank | Advertised Rate | Compounding | True Annual Yield |
|---|---|---|---|
| Online Bank A | 4.50% APR | Monthly | ? |
| Credit Union B | 4.55% APY | Quarterly | ? |
| Digital Bank C | 4.48% APR | Daily | ? |
Step-by-Step Comparison Process
Marcus uses the calculator to find the true annual yield for each option:
Bank A Analysis:
- Enter 4.50% in Input Interest Rate
- Select "Monthly (APR)" for Input Compounding
- Select "Annually (APY)" for Output Compounding
- Click Calculate
- Result: 4.594% APY
Bank B Analysis:
Since this is already APY, Marcus knows the true rate is 4.55%
Bank C Analysis:
- Enter 4.48% in Input Interest Rate
- Select "Daily" for Input Compounding
- Select "Annually (APY)" for Output Compounding
- Result: 4.584% APY
Winner: Bank A offers the highest true return at 4.594% APY, despite having a lower advertised rate than Bank B. This shows why comparing APY (not APR) matters!
Impact of Compounding Frequency
The calculator reveals how the same nominal rate produces different returns based on compounding frequency. Here's what happens to 6% interest with various compounding periods:
| Compounding Frequency | Times Per Year | Effective Annual Rate | $10,000 Becomes |
|---|---|---|---|
| Annually | 1 | 6.000% | $10,600.00 |
| Semiannually | 2 | 6.090% | $10,609.00 |
| Quarterly | 4 | 6.136% | $10,613.64 |
| Monthly | 12 | 6.168% | $10,616.78 |
| Weekly | 52 | 6.180% | $10,617.98 |
| Daily | 365 | 6.183% | $10,618.31 |
| Continuously | ∞ | 6.184% | $10,618.37 |
Notice how the benefit of more frequent compounding diminishes—the jump from annual to monthly is significant ($16.78 extra), but from daily to continuous is minimal ($0.06).
The Dark Side: Credit Card Compounding
While compound interest builds wealth in investments, it devastates finances when you're paying it. Credit cards compound daily, making their true cost higher than the stated APR.
Real Credit Card Scenario
Jennifer has a $5,000 balance on a card advertising "18.99% APR":
Using the Calculator:
• Input: 18.99% Daily compounding
• Output: 20.92% Annually (APY)
• True extra cost: $96 more per year than simple interest
This is why our credit card payoff calculator is essential—it accounts for daily compounding when planning your debt elimination strategy.
Insira aqui imagem ['visual comparison of $5000 credit card debt growth with minimum payments vs aggressive payoff'] , ['Credit Card Debt Compound Interest Effect']
Investment Compounding Strategies
Understanding compounding frequencies helps optimize your investment returns:
CD Ladder Optimization
Banks offer CDs with different compounding terms. Let's compare two 5-year CDs both advertising "3.5%":
CD Option 1: 3.5% APR, compounds annually 5-year value of $10,000: $11,876.86 CD Option 2: 3.5% APR, compounds monthly 5-year value of $10,000: $11,919.85 Difference: $42.99 extra with monthly compounding
For longer terms or larger amounts, this difference becomes substantial. Use our CD calculator to model various scenarios with proper compounding.
Understanding the Math
The calculator uses these formulas for conversions:
Standard Compound Interest:
A = P(1 + r/n)^(nt)
Where: A = final amount, P = principal, r = annual rate, n = compounds per year, t = years
Rate Conversion Formula:
r₂ = n₂ × [(1 + r₁/n₁)^(n₁/n₂) - 1]
Where: r₁ = input rate, n₁ = input frequency, r₂ = output rate, n₂ = output frequency
Continuous Compounding Explained
Continuous compounding represents the mathematical limit—interest calculated and added infinite times per year. While no real account compounds continuously, it's useful for:
- Theoretical calculations in finance - Options pricing models - Understanding maximum possible returns
Formula: A = Pe^(rt), where e ≈ 2.71828 (Euler's number)
Practical Calculator Applications
Beyond simple comparisons, use this calculator for complex financial decisions:
Mortgage Rate Comparison
Mortgages typically compound monthly but quote annual rates. When comparing a 6.5% mortgage to a 6.45% one, the calculator shows:
- 6.5% monthly = 6.697% effective annual rate - 6.45% monthly = 6.646% effective annual rate - True difference: 0.051% annually
On a $300,000 mortgage, this seemingly tiny difference costs $153 more per year. Our mortgage calculator incorporates proper compounding for accurate payment calculations.
Business Loan Analysis
Business loans often have unique compounding terms. A loan advertised as "12% APR, compounded daily" actually costs:
- Effective rate: 12.747% annually - Extra cost on $100,000: $747 per year
Factor loans compound differently—use our business loan calculator for specialized commercial lending scenarios.
Visualizing Compound Growth
The calculator's growth chart shows how $1,000 grows over one year with different compounding frequencies. This visualization helps understand why even small differences in compounding matter over time.
Key patterns to notice: - The curve steepens with more frequent compounding - Early differences seem minimal but accelerate - The gap between frequencies widens over time
Common Compound Interest Misconceptions
The calculator helps clarify frequent misunderstandings:
Myth: "APR and APY are basically the same"
Reality: With monthly compounding, 12% APR = 12.68% APY—that's $68 extra per $10,000!
Other misconceptions the calculator disproves:
- "Daily vs monthly compounding doesn't matter much" (it can be hundreds of dollars annually) - "Banks always quote APY for transparency" (many still use APR to appear competitive) - "Continuous compounding gives dramatically higher returns" (only 0.01-0.02% more than daily)
Maximizing Compound Interest Benefits
Use the calculator insights to optimize your financial strategy:
For Savers and Investors
- Always compare APY, not APR, when choosing accounts
- Prioritize more frequent compounding for long-term investments
- Reinvest dividends to compound returns—our investment calculator models this effect
- Start early—time amplifies compounding more than rate differences
For Borrowers
- Understand true APY cost of daily-compounding debt
- Make payments more frequently than required to reduce compound interest
- Target highest APY debts first, not just highest APR
- Consider biweekly payments to reduce effective compounding
Insira aqui imagem ['side by side comparison showing wealth building through compound interest vs debt growth'] , ['Compound Interest Building Wealth vs Creating Debt']
Advanced Compounding Scenarios
The calculator handles complex situations beyond basic savings:
Variable Rate Analysis
For accounts with changing rates, calculate each period's effective rate separately. A savings account offering "4% for 6 months, then 3%" requires:
1. Convert 4% to effective rate for the initial period 2. Convert 3% for the subsequent period 3. Calculate weighted average based on time
International Rate Comparisons
Different countries quote rates differently. European banks often use effective annual rates, while US banks mix APR and APY. The calculator standardizes these for true comparison.
Pro Tip: When comparing international investment opportunities, always convert to the same compounding basis. A UK account at "5% AER" might beat a US account at "5.1% APR monthly compounding."