Compound Interest Math: How It Actually Works and Why It Matters
Compound interest is the most powerful force in personal finance. After running the numbers for my own savings, I finally understand why. Compound interest is the math behind why long-term investing works and why carrying credit card debt is so expensive. I understood it superficially for years, but running the numbers for my own savings and debts made it click. Here is how the math works, with the calculations I use to make decisions. The Basic Formula The compound interest formula calculates the future value of an amount that grows at a periodic rate. The formula is A equals P times one plus r over n, all raised to the power of n times t. P is the principal, r is the annual rate, n is the number of compounding periods per year, and t is the number of years. A = P * (1 + r/n)^(n*t) P = principal (starting amount) r = annual interest rate (as decimal) n = compounding periods per year t = number of years A = final amount For 10,000 dollars at 5 percent annual interest compounded monthly for 10 years: P is 10000, r is 0.05, n is 12, and t is 10. The result is about 16,470 dollars. The 6,470 dollars of interest is the reward for leaving the money alone, and it grows faster as the years pass because interest earns interest.