Compound Interest Calculator
| Year | Balance | Interest This Year | Total Interest |
|---|---|---|---|
| 1 | $10,830.00 | $830.00 | $830.00 |
| 2 | $11,728.88 | $898.88 | $1,728.88 |
| 3 | $12,702.37 | $973.49 | $2,702.37 |
| 4 | $13,756.66 | $1,054.29 | $3,756.66 |
| 5 | $14,898.46 | $1,141.80 | $4,898.46 |
| 6 | $16,135.02 | $1,236.56 | $6,135.02 |
| 7 | $17,474.22 | $1,339.20 | $7,474.22 |
| 8 | $18,924.57 | $1,450.35 | $8,924.57 |
| 9 | $20,495.30 | $1,570.73 | $10,495.30 |
| 10 | $22,196.40 | $1,701.10 | $12,196.40 |
What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — which only earns on the original deposit — compound interest causes your money to grow at an accelerating rate. Albert Einstein allegedly called it the "eighth wonder of the world," and while that quote is likely apocryphal, the math behind it is genuinely remarkable.
The core mechanic is reinvestment. When interest is credited to your account, it immediately becomes part of the balance that earns future interest. Over long time horizons, this snowball effect can dwarf the original principal. A $10,000 investment at 8% annually grows to $22,196 after 10 years, $46,610 after 20 years, and $98,026 after 30 years — almost ten times the original amount without a single additional dollar contributed.
Compound interest works for you when saving and investing, and against you when borrowing. Credit card debt at 20% APR compounding monthly can double in about 3.8 years if no payments are made. Understanding both sides of the equation is essential for sound personal finance.
Compound Interest Formula
The standard compound interest formula for a lump-sum principal without additional contributions is:
A = P(1 + r/n)nt
Where each variable means:
| Variable | Meaning | Example |
|---|---|---|
| A | Final amount (future value) | $22,196.40 |
| P | Principal (initial investment) | $10,000 |
| r | Annual interest rate (as a decimal) | 0.08 (= 8%) |
| n | Number of compounding periods per year | 12 (monthly) |
| t | Time in years | 10 |
Worked Example — Step by Step
Calculate the future value of $10,000 at 8% annual interest, compounded monthly, over 10 years:
Formula with Additional Contributions
When you make regular contributions at each compounding period, the future value formula expands to include a second term:
A = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
Where PMT is the contribution per compounding period. If you contribute monthly to a monthly-compounding account, PMT equals your monthly deposit. The second term is essentially the future value of an annuity — a series of equal payments each growing for a different number of periods.
Compounding Frequency — Does It Matter?
The more frequently interest compounds, the higher the final balance — but the gains from increasing frequency follow the law of diminishing returns. The jump from annual to monthly compounding is significant; the jump from monthly to daily is marginal.
The table below compares $10,000 invested at 8% for 10 years across different compounding frequencies:
| Compounding Frequency | Periods per Year (n) | Future Value | Total Interest | Effective Annual Rate |
|---|---|---|---|---|
| Annually | 1 | $21,589.25 | $11,589.25 | 8.0000% |
| Semi-Annually | 2 | $21,911.23 | $11,911.23 | 8.1600% |
| Quarterly | 4 | $22,079.44 | $12,079.44 | 8.2432% |
| Monthly | 12 | $22,196.40 | $12,196.40 | 8.3000% |
| Daily | 365 | $22,253.46 | $12,253.46 | 8.3278% |
Moving from annual to monthly compounding adds $607.15 to the final balance — that's meaningful. Moving from monthly to daily adds only $57.06. When comparing savings accounts or certificates of deposit, always look at the APY (Annual Percentage Yield) rather than the nominal rate, since APY already incorporates the compounding frequency and lets you compare products directly.
Note that continuously compounded interest — the mathematical limit as n approaches infinity — uses the formula A = Pert. For 8% over 10 years: A = 10,000 × e0.8 = $22,255.41. This is only $2 more than daily compounding, confirming how quickly the gains plateau.
The Rule of 72
The Rule of 72 is a mental math shortcut that tells you how many years it takes to double your money at a given annual interest rate:
Years to double ≈ 72 ÷ Annual Rate (%)
Examples:
| Annual Rate | Rule of 72 Estimate | Exact Years |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
The exact formula is: Years = ln(2) / ln(1 + r) where r is the rate as a decimal. The Rule of 72 is most accurate between 6% and 10%. Outside that range, some analysts prefer the Rule of 69.3 (which is ln(2) × 100 = 69.3), or adjust empirically — the Rule of 70 works well at lower rates.
The Rule of 72 also works in reverse: if you want to know what rate you need to double your money in a given number of years, divide 72 by the years. Want to double in 8 years? You need approximately 72 / 8 = 9% annual return.
Frequently Asked Questions
What is the difference between simple interest and compound interest?
Simple interest is calculated only on the original principal: I = P × r × t. Compound interest is calculated on the principal plus all previously accumulated interest, so your earnings grow exponentially over time. On $10,000 at 8% for 10 years, simple interest yields $8,000 in interest while monthly compounding yields $12,196.40 — roughly 52% more.
How often should interest compound to maximize my returns?
More frequent compounding means slightly higher returns. Daily compounding produces the maximum return for a given annual rate. However, the difference between monthly and daily compounding is tiny — on $10,000 at 8% for 10 years, daily compounding adds only about $11 more than monthly. Annual vs. monthly compounding is the bigger gap (~$440 on the same example).
What is the Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR), also called the Annual Equivalent Rate (AER), is the actual annual return accounting for compounding. Formula: EAR = (1 + r/n)^n - 1. For 8% compounded monthly: EAR = (1 + 0.08/12)^12 - 1 = 8.3000%. This lets you compare accounts with different compounding frequencies on an equal basis.
Does the Rule of 72 work for compound interest?
Yes. The Rule of 72 is a shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 8%, money doubles in approximately 72 / 8 = 9 years. The exact answer using the compound interest formula is ln(2) / ln(1.08) = 9.006 years — the rule is remarkably close. The rule is most accurate for rates between 6% and 10%.
How do additional contributions affect compound interest growth?
Additional contributions accelerate growth significantly because each new deposit immediately starts compounding. The future value of periodic contributions follows: FV = PMT × [((1 + r/n)^(nt) - 1) / (r/n)]. Adding just $100/month to a $10,000 principal at 8% for 10 years grows the final balance from $22,196 to $40,592 — an extra $12,000 contributed generates an additional $18,396 in total value.
What is a good compound interest rate to expect?
Historical reference points: US savings accounts average 0.5–5% (varies with Fed rate); CDs typically 4–5.5%; bonds 3–5%; S&P 500 historical average ~10% nominal (~7% inflation-adjusted). Always compare the APY (Annual Percentage Yield), which equals the Effective Annual Rate and already accounts for compounding frequency.
Related Calculators
- Savings Calculator — Set a savings goal and calculate how long it will take to reach it
- Investment Calculator — Project returns on lump-sum and recurring investments
- Simple Interest Calculator — Calculate interest on principal only (P × r × t)
- 401(k) Calculator — Model retirement savings with employer match and contribution limits
- SIP Calculator — Systematic Investment Plan future value for monthly contributions