Compound Interest Calculator
Calculate compound interest to simulate investment growth. Enter principal, rate, term, and optional contributions.
Compound interest is the engine of long-term wealth building — interest earned itself earns interest, creating exponential growth. This calculator simulates returns across savings accounts, ETFs, IRAs, 401(k)s, and any long-term investment with optional monthly contributions. Configure five compounding frequencies (annual, semi-annual, quarterly, monthly, daily), see year-by-year breakdowns, and check the Rule of 72 along with the effective annual rate (EAR). Use it for retirement planning, FIRE goals, college savings, or comparing CDs and high-yield savings accounts.
📖 How to Use
- Enter the principal amount
- Enter the annual interest rate (%)
- Enter the investment period in years
- Select the compounding frequency (monthly recommended)
- Optionally enter monthly contribution amount
- View the final amount and yearly growth breakdown
✨ Features
- ✓Compound interest formula A = P(1 + r/n)^(nt)
- ✓5 compounding frequencies (annually, semi-annually, quarterly, monthly, daily)
- ✓Monthly contribution option for regular savings
- ✓Year-by-year growth table
- ✓Visual breakdown of principal/contributions/interest
- ✓Effective Annual Rate (EAR) calculation
📐 Formula
A = P(1 + r/n)^(nt) + PMT × [(1 + r/n)^(nt) - 1] / (r/n)💡 How It Works
- •Compound interest means earning interest on both the principal and accumulated interest.
- •In the formula A = P(1 + r/n)^(nt), P is principal, r is annual rate, n is compounding periods per year, t is time in years.
- •More frequent compounding (daily > monthly > annually) yields higher returns.
- •Effective Annual Rate (EAR) reflects the true annual return including compounding. EAR = (1 + r/n)^n - 1
- •Rule of 72: Years to double ≈ 72 ÷ interest rate (%)
- •In long-term investing, compound interest grows exponentially (the 'magic of compounding').
📊 Real-world Examples
$10,000 principal, 5% monthly compounding, 10 years
10,000 × (1 + 0.05/12)^(12×10)
→ ≈ $16,470 (gain $6,470, +64.7%)
$5,000 start + $500/mo contributions, 7% annual, 30 years
5,000 × (1.0058)^360 + 500 × [(1.0058)^360 − 1] / 0.0058
→ ≈ $646,890 (contributions $185k, interest $462k)
Retirement target $1M in 25 years at 6% — monthly need
PMT = 1,000,000 / [((1.005)^300 − 1) / 0.005]
→ ≈ $1,443/month
Rule of 72: doubling time at 6% annual
72 ÷ 6 = 12
→ About 12 years (exact compound: 11.9)
🎯 Use Cases
- ▸Project tax-advantaged accounts (401(k), Roth IRA, HSA) to retirement
- ▸Estimate ETF and index-fund growth with monthly DCA contributions
- ▸Calculate FIRE numbers — savings required to retire early
- ▸Compare CDs vs high-yield savings vs Treasury bills net yield
- ▸Plan 529 college savings contributions for a target date
- ▸Visualize long-term stock or crypto holdings (Bitcoin DCA scenarios)
⚠️ Common Mistakes
Mistake: Using annual compounding when most accounts compound monthly or daily
Correct: Banks and brokerages typically compound monthly or daily. Using annual compounding underestimates returns by ~1-2% over long horizons. Match the frequency to your account terms.
Mistake: Ignoring taxes on interest and capital gains
Correct: US ordinary interest is taxed as income (10-37%). Long-term capital gains are 0/15/20%. Tax-advantaged accounts (Roth IRA, 401k) defer or eliminate tax. Subtract ~1-2% from gross yields for realistic after-tax projections.
Mistake: Treating average market return as guaranteed yield
Correct: Stock market averages ~7% real return, but with high variance — some years -20%, others +30%. Sequence-of-returns risk matters for retirees. Use 4-5% conservative rates for safe planning.
Mistake: Forgetting to adjust for inflation
Correct: Assuming 2-3% inflation, real return = nominal − inflation. $1M in 30 years equals roughly $412k in today's purchasing power (3% inflation). Plan in real, not nominal, terms.
❓ FAQ
Q. What's the difference between simple and compound interest?
A. Simple interest is calculated only on the principal, while compound interest is calculated on principal plus accumulated interest. Compound interest is much more beneficial for long-term investments.
Q. Is monthly or annual compounding better?
A. More frequent compounding is better. At 5% annual rate, annual compounding gives 5% effective rate, while monthly compounding gives 5.12%.
Q. What is the Rule of 72?
A. A quick way to estimate how long it takes to double your money: 72 ÷ interest rate (%) = years to double. For example, at 6% it takes about 12 years.
Q. What will $10,000 become at 5% for 10 years?
A. With monthly compounding, approximately $16,470. That's about 65% return on the principal.
Q. Why is regular investing beneficial?
A. Regular monthly contributions help spread market volatility (dollar-cost averaging) and maximize the compound interest effect.
Q. What about taxes?
A. This calculator shows pre-tax returns. Investment gains are typically subject to capital gains tax, which varies by country and holding period.
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