Compound Interest vs Simple Interest: Complete Guide
Interest is the compensation paid or earned for the use of money. There are two fundamental types, and understanding the difference is essential for anyone borrowing or investing.
Simple Interest
Simple interest is calculated only on the original principal - never on accumulated interest. It is straightforward and predictable:
I = P ร r ร t
I = interest earned ยท P = principal ยท r = annual rate (decimal) ยท t = time in years
Example: $10,000 at 5% for 3 years โ I = $10,000 ร 0.05 ร 3 = $1,500 โ Total: $11,500
Simple interest is commonly used for short-term personal loans, auto loans (in some structures), and Treasury bills. It's predictable and transparent - your interest charge is the same every period.
Compound Interest
Compound interest is calculated on the principal plus any interest already accumulated. This creates exponential growth - you earn "interest on interest." The more frequently interest compounds, the more you earn (or owe):
A = P(1 + r/n)^(nt)
A = final balance ยท P = principal ยท r = annual rate (decimal) ยท n = compounding periods/year ยท t = years
Example: $10,000 at 5% for 3 years, monthly compounding โ A = $10,000 ร (1 + 0.05/12)^36 = $11,614.72
Continuous Compounding
The theoretical limit of compounding - interest is calculated and added at every possible instant. While no real financial product compounds continuously, it's an important mathematical concept:
A = Pe^(rt)
e โ 2.71828 (Euler's number) ยท Example: $10,000 at 5% for 3 years โ A = $10,000 ร e^(0.15) = $11,618.34
Compounding Frequency Comparison
The effect of compounding frequency on $10,000 at 5% over 10 years:
| Frequency | Periods/Year | Ending Balance | Interest Earned | Effective APY |
|---|
| Annually | 1 | $16,288.95 | $6,288.95 | 5.000% |
| Semi-annually | 2 | $16,386.16 | $6,386.16 | 5.063% |
| Quarterly | 4 | $16,436.19 | $6,436.19 | 5.095% |
| Monthly | 12 | $16,470.09 | $6,470.09 | 5.116% |
| Daily | 365 | $16,486.65 | $6,486.65 | 5.127% |
| Continuously | โ | $16,487.21 | $6,487.21 | 5.127% |
The Rule of 72 - How Long to Double Your Money
The Rule of 72 is a quick mental math trick to estimate how long it takes to double your money at a given compound interest rate:
Doubling time (years) โ 72 รท annual interest rate (%)
Example: At 6%, money doubles in โ 72 รท 6 = 12 years. At 9%, โ 8 years. At 12%, โ 6 years.
| Annual Rate | Rule of 72 (approx) | Exact Doubling Time |
|---|
| 2% | 36.0 years | 35.0 years |
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
APR vs APY: Understanding the Difference
APR (Annual Percentage Rate) is the stated, nominal interest rate - it does not account for compounding within the year.
APY (Annual Percentage Yield) is the effective annual rate after compounding. It's always โฅ APR (equal only if compounding is annual):
APY = (1 + APR/n)^n - 1
Where n = compounding periods per year
Example: 6% APR, monthly compounding โ APY = (1 + 0.06/12)^12 - 1 = 6.168%
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When comparing savings accounts or investments, always compare APY, not APR. A 5.0% APR compounded daily earns more than a 5.0% APR compounded annually, and APY captures this difference.
Inflation & Taxes: Real Returns on Your Investment
The Impact of Inflation
Inflation erodes the purchasing power of your money over time. Even if your investment earns 6% annually, if inflation is 3%, your real return is approximately:
Real Return โ (1 + nominal rate) รท (1 + inflation rate) - 1
Example: 6% nominal, 3% inflation โ (1.06 รท 1.03) - 1 = 2.91% real return
The inflation-adjusted balance shown in this calculator represents what your ending balance is worth in today's purchasing power. For long-term planning (20-30 years), inflation has a massive impact - at 3% inflation, $100,000 in 20 years is worth only ~$55,000 in today's dollars.
Taxes on Interest Income
Interest income from savings accounts, CDs, and bonds is typically taxed as ordinary income in the US. If you're in the 22% tax bracket and earn $5,000 in interest, you keep only $3,900 after taxes. This significantly reduces effective yield:
| Nominal Rate | Tax Bracket | After-Tax Rate | APY After Tax |
|---|
| 5% | 22% | 3.90% | 3.94% (monthly) |
| 5% | 32% | 3.40% | 3.46% (monthly) |
| 5% | 37% | 3.15% | 3.20% (monthly) |
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Tax-advantaged accounts first: Growth in a 401(k), IRA, Roth IRA, or HSA is sheltered from annual tax, making compound growth far more powerful. Max these accounts before keeping money in taxable savings for long periods.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the principal and the previously accumulated interest. Unlike simple interest, which only applies to the original principal, compound interest causes exponential growth - you earn "interest on interest." Over long time periods, this dramatically increases your returns. Einstein reportedly called compound interest the "eighth wonder of the world."
How does compounding frequency affect my returns?
The more frequently interest compounds, the higher your effective annual yield (APY). Monthly compounding earns more than annual compounding at the same stated rate. However, the differences between daily and monthly compounding are very small - the big jump in yield comes from moving from annual to monthly. Use this calculator to compare frequencies directly.
How do I calculate interest on savings?
For savings accounts: use the compound interest formula A = P(1 + r/n)^(nt). Enter your initial deposit (P), the annual interest rate (r), how often interest compounds (n), and the time period (t). For ongoing deposits, add your monthly or annual contribution amounts. This calculator handles all these inputs and shows a full month-by-month accumulation schedule.
Is compound interest good or bad?
Compound interest works FOR you when you're saving or investing (your money grows exponentially). It works AGAINST you when you're borrowing - credit card debt at 20% APR compounding daily can cause balances to double in under 4 years. The key lesson: save and invest early (to benefit from compounding), and pay off high-interest debt quickly (to avoid being punished by it).
What is the effective annual rate (EAR)?
EAR (also called APY or effective annual yield) is the actual annual return accounting for compounding. Formula: EAR = (1 + r/n)^n - 1. For example, 6% APR compounded monthly gives EAR = (1 + 0.06/12)^12 - 1 = 6.168%. EAR is the true "apples-to-apples" comparison number when evaluating different accounts or investments.
