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Calculate compound interest and future investment value
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Compound interest grows your investment by applying interest to both the original principal and all previously earned interest. The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is compounding periods per year (daily=365, monthly=12, quarterly=4, annually=1), and t is time in years. Daily compounding produces slightly more than monthly, which produces slightly more than annual. A classic example: $10,000 invested at 7% annual return compounded monthly grows to $20,097 after 10 years. The Rule of 72 estimates doubling time: divide 72 by the annual interest rate to get the approximate years to double your money.
1. Enter your principal (initial investment amount). 2. Enter the annual interest rate as a percentage. 3. Select the compounding frequency (daily, monthly, quarterly, or annually). 4. Enter the investment time period in years. 5. Optionally enter regular additional contributions. 6. Click Calculate to see the final amount, total interest earned, and growth breakdown.
The compound interest formula is A = P(1 + r/n)^(nt), where: A = final amount, P = principal (initial investment), r = annual interest rate as a decimal (e.g., 7% = 0.07), n = compounding periods per year (daily=365, monthly=12, quarterly=4, annually=1), t = time in years. Total interest earned = A - P. For $10,000 at 8% compounded monthly for 5 years: A = 10000(1 + 0.08/12)^(60) = $14,898.
More frequent compounding produces slightly higher returns. For $10,000 at 10% annual rate over 10 years: annually = $25,937; quarterly = $26,851; monthly = $27,070; daily = $27,179. The difference between monthly and daily is small (about $109 over 10 years), but the gap between annual and monthly compounding is more significant ($1,133 over 10 years). For long time horizons, monthly or daily compounding noticeably outperforms annual.
The Rule of 72 is a mental math shortcut to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate. At 6% annual return, your money doubles in approximately 72 ÷ 6 = 12 years. At 9%, it doubles in 8 years. At 12%, about 6 years. The rule is accurate within about 1% for rates between 6% and 10%. It works because the natural log of 2 (0.693) approximates to 72/100 of the interest rate.
APR (Annual Percentage Rate) is the simple stated interest rate without accounting for compounding. APY (Annual Percentage Yield, also called EAR or effective annual rate) reflects the actual annual return after compounding. A savings account with 5% APR compounded monthly has an APY of (1 + 0.05/12)^12 - 1 = 5.116%. When comparing savings accounts or investments, always compare APY — it is the true rate of return and accounts for compounding frequency.
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A typical scenario using default values
{
"principal": 10000,
"annual_rate": 5,
"years": 10,
"compound_frequency": 12
}