Compound Interest Calculator
Calculate investment growth with compound interest.
How to Use the Compound Interest Calculator
Compound interest is one of the most powerful forces in personal finance. Albert Einstein reportedly called it the "eighth wonder of the world." This calculator lets you see exactly how money grows over time when interest is reinvested, and shows a year-by-year breakdown of your investment's growth.
The Compound Interest Formula
The formula is: A = P × (1 + r/n)^(n×t), where:
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate (as a decimal, e.g., 0.07 for 7%)
- n = Number of times interest compounds per year
- t = Time in years
Compounding Frequency
More frequent compounding produces slightly higher returns. Daily compounding (365x/year) produces slightly more than monthly (12x/year), which produces more than quarterly (4x/year), which produces more than annually (1x/year). The differences are small at typical interest rates but become more significant at higher rates or over longer periods. Most savings accounts compound daily or monthly; most bonds and certificates of deposit compound semi-annually.
The Power of Time
The year-by-year table reveals a key insight: interest earned accelerates over time. In early years, most of your growth is from the original principal. In later years, the interest earned on previous interest begins to dominate. This is why starting to invest early, even with small amounts, is so much more powerful than waiting and investing larger amounts later.
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Frequently Asked Questions
What's the Rule of 72?
The Rule of 72 is a quick mental math shortcut: divide 72 by your annual interest rate to find approximately how many years it takes to double your money. For example, at 7% annual return, 72 ÷ 7 ≈ 10.3 years to double. At 10%, it takes about 7.2 years. At 4%, about 18 years. This rule is accurate for rates between 3–12% and annual compounding.
What's the difference between compound and simple interest?
Simple interest is calculated only on the principal: Interest = P × r × t. For example, $10,000 at 5% for 10 years = $5,000 total interest ($15,000 total). Compound interest reinvests earned interest so it also earns interest. The same example with annual compounding = $10,000 × (1.05)^10 = $16,289 — $1,289 more. Over longer periods, the difference becomes dramatic.
Does this account for regular contributions?
No, this calculator only models a one-time lump sum investment (the principal). For calculations with regular monthly or annual contributions (like a retirement account), you would need the future value of annuity formula: FV = PMT × [((1 + r/n)^(n×t) − 1) / (r/n)], added to the lump sum formula. This is a more complex calculation not covered here.
What's a realistic interest rate to use?
For long-term stock market investments: historically, the S&P 500 has averaged about 10% annually before inflation (7% after inflation). For bonds: 3–5%. For high-yield savings accounts: 4–5% (as of 2024). For regular savings accounts: 0.5–1%. For CDs: 4–5%. For real estate: varies widely but historically 3–5% appreciation. Use realistic rates for your specific investment type.
Should I choose daily or monthly compounding?
For typical interest rates (1–10%), the difference between daily and monthly compounding is very small. On $10,000 at 5% for 10 years: daily compounding gives $16,487, monthly gives $16,470 — a difference of just $17. At higher rates, the difference is larger but still modest. Choose the frequency that matches your actual account type for accurate projections.