Compound interest

Compound interest is when you earn interest on the money you've saved and on the interest you earn along the way ¹. At 5% a year, $1,000 becomes $1,050 after one year and $1,102.50 after two, because the second year's interest is calculated on the new value ². The total is A = P(1 + r/n)^(nt), where r is the yearly rate and n how many times a year interest is added ³. Adding it more often helps only a little: as n grows without limit, the effective rate approaches an upper limit ⁴. Jacob Bernoulli found the constant e in 1683 studying this question ⁵.

To estimate the years to double, divide 72 by the yearly rate, a rule Luca Pacioli printed in 1494 ¹; 72 works well in common interest situations and divides easily ². Time is the big lever. In a Retraite Québec example at 5% a year, Stephanie saves $1,000 a year from 25 to 35, $10,000 in all, and has $61,400 at 65 ³⁴. Frank saves $1,000 a year for 20 years from 45, $20,000 in all, and has $35,700 ⁵.

Compounding also describes the accumulation of debts from a borrower ¹. Many credit card companies calculate the interest you owe daily, based on your average daily account balance ², so the sooner you pay off all or some of a balance, the less interest you pay ³. Lenders charging compound interest was once regarded as the worst kind of usury ⁴. By the rule of 72, an unpaid balance at 24% a year doubles in about three years.