Definition: Compound interest is interest earned on both the original principal and the interest already added, giving the exponential model A = P(1 + r/n)^(nt).
How does compounding work?
After each period, the interest is added to the balance. The next interest is then computed on the larger amount. That is why money grows faster than with simple interest, which always uses the original principal.
What do the letters mean?
P is the starting amount, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years.
Example. Invest 2,500 dollars at 4.8% compounded monthly for 6 years. Here r/n = 0.048/12 = 0.004 and nt = 72. So A = 2500(1.004)72. Since 1.00472 is about 1.3328, A is about 3,332 dollars. Simple interest would give 2500 + 2500(0.048)(6) = 3,220 dollars.
What do students mix up?
Using r = 4.8 instead of 0.048, or forgetting to divide the rate by n. Another error is writing the exponent as t when interest is compounded more than once a year. For continuous situations, a different formula with the number e is used in later courses.