Compound Interest Calculator

Simple interest is calculated solely on the original principal amount, producing linear growth over time. The formula is A = P(1 + rt), where interest accrues only on the initial principal each period. Compound interest, by contrast, is calculated on both the principal and the accumulated interest from prior periods, following the formula A = P(1 + r)^t. This means each period’s interest is added to the principal, and subsequent interest is earned on the growing balance. Over a 30-year horizon, a $10,000 investment at 7% grows to just $31,000 with simple interest, but to over $76,000 with annual compounding — more than double. The exponential nature of compounding means the gap widens dramatically over time: the first 10 years show a modest difference, but the following decades produce increasingly divergent outcomes. This is why Albert Einstein reportedly called compound interest the “eighth wonder of the world.” Understanding this distinction is fundamental to long-term wealth building.

— Source: SEC.gov, Investor.gov — Compound Interest

The Rule of 72 is a powerful mental math shortcut that estimates how many years it takes for an investment to double at a fixed annual rate of return. The formula is remarkably simple: t ≈ 72 / r, where t is the doubling time in years and r is the annual return expressed as a whole number. At 8% annual return: 72 ÷ 8 ≈ 9 years. At 6%: 72 ÷ 6 ≈ 12 years. The rule also works in reverse to determine the required rate of return for a desired doubling period: r ≈ 72 / t. If you want your portfolio to double in 10 years, you need approximately 72 ÷ 10 = 7.2% annual return. In real-world investing, the Rule of 72 helps quickly compare investment opportunities: a stock fund averaging 9% doubles in 8 years, while a bond yielding 3% takes 24 years. It also illustrates the devastating effect of fees — a 1% management fee reduces an 8% return to 7%, extending the doubling time from 9 years to nearly 10.3 years. The rule is most accurate for rates between 4% and 15%, with error margins under 0.5 years. For more precise calculations, use the natural logarithm formula: t = ln(2) / ln(1 + r/100).

— Source: Investopedia — Rule of 72

Yes, monthly compounding produces higher returns than annual compounding, and the advantage grows with time. The general compound interest formula is A = P(1 + r/n)^(nt), where n is the compounding frequency. Monthly compounding means n = 12, so interest is calculated and added to your balance 12 times per year. Each month's interest begins earning its own interest immediately, creating a compounding-on-compounding effect. A $100,000 investment at 5% yields $164,701 after 10 years with monthly compounding versus $162,889 annually — a difference of $1,812. Extend this to 20 years: $271,264 monthly vs $265,330 annually, a $5,934 gap. At 30 years: $446,774 monthly vs $432,194 annually, a $14,580 difference. The absolute gap increases with each decade because the compounding base grows larger. For most long-term investors, monthly compounding adds meaningful value without requiring any additional effort or risk. The takeaway: choose monthly compounding whenever available, especially for retirement accounts and long-term savings vehicles.

— Source: SEC.gov — The Power of Compound Interest

Inflation is the silent eroder of investment returns, and its impact on compounding is profound over multi-decade horizons. While compound interest grows your nominal balance, inflation progressively reduces what that money can actually purchase. The real rate of return is calculated using the Fisher equation: (1 + r_nominal) = (1 + r_real)(1 + i), which simplifies to r_real ≈ r_nominal - i for low rates. At a 7% nominal return with 3% annual inflation, the real return is approximately 4%. While this 3% gap may seem small, its compounded effect is devastating: a $100,000 investment growing at 7% nominal over 30 years reaches $761,226 on paper. However, after adjusting for 3% inflation, the real purchasing power is only about $313,000 in today’s dollars — less than half the nominal figure. Extending to 40 years at the same rates, the nominal balance reaches $1,497,445, but the inflation-adjusted value drops to just $459,000. This means over 65% of the nominal gain is consumed by inflation. The practical implication is critical: investors must target nominal returns that significantly exceed inflation to build real wealth. This is why conservative fixed-income investments yielding 2-3% may actually lose purchasing power after taxes and inflation.

— Source: U.S. Bureau of Labor Statistics — CPI Data; Investopedia — Inflation

When you make monthly contributions, each contribution starts earning interest immediately (with monthly compounding) or at the end of the year (with yearly compounding). The formula combines the compound interest on the initial principal with the future value of a series of monthly payments. This is why regular contributions significantly boost long-term returns.

Compound interest is dramatically more powerful for long-term investing because of the exponential growth curve. The majority of growth happens in the later years. For example, a $10,000 investment at 7% grows to $19,672 after 10 years, but to $76,123 after 30 years — even though only 20 more years have passed. Time is the most important factor in compounding.

Historically, the US stock market (S&P 500) has returned about 7-10% annually on average over long periods. High-yield savings accounts typically offer 3-5%. Bond investments usually return 3-6%. The "best" rate depends on your risk tolerance and investment horizon. Higher potential returns come with higher risk.