Compound Interest Calculator
Calculate compound interest with optional monthly contributions. See year-by-year growth breakdown using the formula A = P(1 + r/n)^(nt).
Results
Final Balance
$48,357.54
$14,357
Total Interest
Principal
Contributions
Interest
Initial Principal
$10,000
Total Contributions
$24,000
Total Interest
$14,357.54
APY
7.23%
Compound Interest Formula
A = P(1 + r/n)^(nt)
P = principal, r = rate, n = compounds/year, t = years
Year-by-Year Breakdown
| Year | Deposits | Interest | Total Interest | Balance |
|---|
Understanding Compound Interest
Compound Interest Formula
A = P(1 + r/n)^(nt)
Where A is the final amount, P is principal, r is annual rate (decimal), n is compounds per year, and t is time in years.
APY Calculation
APY = (1 + r/n)^n - 1
Annual Percentage Yield shows your actual yearly return including compounding effects. Higher compounding frequency = higher APY.
Rule of 72
Years to Double = 72 / Interest Rate
Quick estimate for doubling time. At 7% interest, your money doubles in approximately 72/7 = 10.3 years.
Frequently Asked Questions
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest which only earns interest on the principal, compound interest allows your money to grow exponentially over time as you earn "interest on interest." This is often called the "eighth wonder of the world" because of its powerful wealth-building potential.
The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the time in years. For example, $10,000 at 5% compounded monthly for 10 years: A = 10000(1 + 0.05/12)^(12*10) = $16,470.09.
The more frequently interest compounds, the more you earn. Daily compounding earns slightly more than monthly, which earns more than quarterly, which earns more than annually. For example, $10,000 at 5% for 10 years yields: $16,288.95 (annual), $16,436.19 (quarterly), $16,470.09 (monthly), and $16,486.65 (daily). The difference becomes more significant with higher interest rates and longer time periods.
APR (Annual Percentage Rate) is the simple interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compounding and shows the actual yearly return. For example, a 5% APR compounded monthly has an APY of 5.116%. When comparing savings accounts or investments, always compare APY for an accurate comparison of returns.
Regular monthly contributions dramatically accelerate wealth building due to compound interest. Each contribution starts earning its own compound interest immediately. For example, $10,000 initial investment at 7% for 20 years grows to $38,697. But adding just $200/month in contributions grows that to $142,797 - the contributions plus compound interest on those contributions add over $100,000 to your final balance.