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Kalcufy

Compound Interest Calculator

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods — earning 'interest on interest.' Unlike simple interest (which only earns on the original amount), compound interest creates exponential growth because each interest payment increases the base amount for the next calculation. Albert Einstein reportedly called compound interest 'the eighth wonder of the world.' Over long time horizons, the difference between simple and compound interest becomes dramatic: $10,000 at 8% simple interest earns $800/year forever, while at 8% compound interest it doubles roughly every 9 years, growing to $46,610 in 20 years vs $26,000 with simple interest.

How the Compound Interest Formula Works

The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate (decimal), n is the compounding frequency per year, and t is years. When you add regular contributions (PMT), the future value of an annuity formula is added: PMT × [((1 + r/n)^(nt) − 1) / (r/n)]. The key insight is that higher compounding frequency (n) means the exponent grows faster: daily compounding at 5% yields an effective rate of 5.127%, while annual compounding stays at exactly 5%. This calculator separates 'interest from principal' and 'interest on interest' so you can see exactly how much of your earnings come from the compounding effect alone.

Frequently Asked Questions

What is compound interest and how does it differ from simple interest?

Compound interest calculates interest on both the original principal and all previously earned interest — 'interest on interest.' Simple interest only calculates on the original principal. Example: $10,000 at 5% for 10 years earns $5,000 in simple interest but $6,289 in compound interest (annually) — that extra $1,289 is the interest earned on interest.

How does compounding frequency affect my returns?

More frequent compounding means slightly higher effective returns. At 5% nominal rate: annual compounding yields 5.00% APY, monthly yields 5.12%, daily yields 5.13%. The difference is small at low rates but compounds significantly over long periods. For a $100,000 investment over 30 years at 7%, daily vs annual compounding means roughly $10,000 more.

What is the Rule of 72 and how accurate is it?

The Rule of 72 estimates how many years it takes to double your money: divide 72 by the annual interest rate. At 8%, money doubles in ~9 years (72÷8=9). It's most accurate for rates between 6-10%. For rates below 5%, use the Rule of 70 instead. The rule works for annual compounding; daily compounding doubles slightly faster.

What is APY (Annual Percentage Yield) vs APR?

APR (Annual Percentage Rate) is the stated nominal interest rate. APY (Annual Percentage Yield) is the effective rate after accounting for compounding frequency. APY is always ≥ APR. A credit card at 24% APR compounded daily has an APY of 27.11%. When comparing investments, always compare APY to APY for a fair comparison.

How does inflation affect my compound interest returns?

Inflation reduces the purchasing power of future money. At 3% inflation, $100,000 in 20 years only buys what $55,368 buys today. To find your 'real' return, subtract inflation from your nominal rate: 8% return − 3% inflation ≈ 5% real return. This calculator shows both nominal and inflation-adjusted values so you can plan realistically.

Should I contribute monthly or invest a lump sum?

Mathematically, a lump sum invested immediately earns more because it compounds for the full period. However, most people don't have a lump sum available. Dollar-cost averaging (regular monthly contributions) is the practical approach for building wealth and also smooths out market volatility. The key is consistency — automate contributions and don't try to time the market.

How much should I invest to reach a specific goal?

Use this calculator in reverse: enter your target amount as the future value and adjust the initial investment and monthly contributions until you reach it. For example, to have $1M in 30 years at 8% annual return, you'd need either ~$99,400 today with no contributions, or ~$670/month starting from $0. Starting with $10,000 + $500/month gets you there too.

What is 'interest on interest' and why does it matter?

Interest on interest is the portion of your earnings generated by previously earned interest — not by your original deposits. It's the core mechanism of compounding. Over long periods, it becomes the majority of your returns: in a 30-year investment at 8%, about 75% of your final balance is interest on interest. This is why time is the most powerful factor in wealth building.