Compound interest: earning interest on interest

0:00You save 1000 dollars at 4 percent a year. How much do you have after 10 years?

0:07The principal is the 1000 dollars you start with. Interest is what the bank pays you to use your money.

0:14Simple interest pays 4 percent of the principal only: 40 dollars every year.

0:21After 10 years you have 1000 plus 10 times 40, which is 1400 dollars. On the graph, that is a straight line.

0:32Compound interest adds each year's interest to the money in the account, so the interest earns interest too.

0:40Adding 4 percent means multiplying by 1.04. Year 1: 1000 times 1.04 is 1040 dollars. Year 2: 1040 times 1.04 is 1081 dollars and 60 cents.

0:58So year 2 earns 41 dollars and 60 cents: 40 dollars, plus 1 dollar 60, which is 4 percent of last year's 40.

1:08Ten years means multiplying by 1.04 ten times: 1000 times 1.04 to the power of 10 is 1480 dollars and 24 cents.

1:22On the graph it is a curve that bends upward, because each year's interest is bigger than the last.

1:29Compounded monthly, the bank adds 4 percent divided by 12 every month, 120 times. You get 1490 dollars and 83 cents.

1:41A common mistake: 4 percent times 10 years is 40 percent, so 1000 times 1.4 is 1400. That is simple interest, not compound.

1:54Compound interest earns interest on interest: 1000 dollars at 4 percent for 10 years becomes 1480 dollars and 24 cents.