What is the compound interest formula?
A = P(1 + r/n)^(nt), where P = principal, r = annual interest rate (decimal), n = compounding frequency per year (12 = monthly, 365 = daily), and t = time in years. For example, $10,000 at 7% compounded monthly for 20 years grows to $40,388.
What is the Rule of 72?
Divide 72 by your annual interest rate to estimate how many years it takes for money to double. At 6%, money doubles in 72 ÷ 6 = 12 years. At 10%, it doubles in just 7.2 years. It works for any compound interest rate.
How often should interest compound for the best returns?
More frequent compounding slightly increases returns. Daily compounding earns about 0.5% more per year than annual compounding at the same stated rate. In practice, the difference between monthly and daily is tiny — what matters most is the interest rate itself.
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the stated annual rate before compounding effects. APY (Annual Percentage Yield) reflects the actual return including compounding. A 6% APR compounded monthly = 6.17% APY. Banks advertise APY for savings accounts because it looks higher.
What is the difference between simple and compound interest?
Simple interest is paid only on the original principal — it does not snowball. Compound interest earns interest on both the principal and all accumulated interest, which is why long-term investments grow exponentially. On a $10,000 30-year deposit at 5%, simple interest yields $15,000 extra; compound yields $43,219.
How much will $1,000 grow to in 30 years?
At 5% compounded annually, $1,000 grows to $4,322. At 7%, it reaches $7,612. At 10% (S&P 500 historical average), it grows to $17,449. Starting early is more powerful than a higher rate — $1,000 invested at 25 instead of 35 at the same rate results in roughly twice the final amount.