Suppose there is a bank that will give you a great [underlying] rate of interest on your deposit: let us say 100% per year. Yes, I know that is an outrageous hypothetical, but humor me. If you give this "Bank of Euler" $1 on Dec. 31, then on the following Dec. 31 you can withdraw $2. Great! But, even better, the bank offers a half-year compounding. You can give the bank $1. on Dec. 31. On the following July 1 the bank will calculate your interest so far, and thereafter your interest will compound onto that new figure. This means that on July 1 they gave you half of the annual amount due you. In this case: fifty cents. So as of July 1 you have $1.50 in the bank. The rest of the year you earn NOT the other 50 cents, but half of the annual rate on that new number. This is $0.75. On Dec. 31, then, you will have the original $1.00 plus the mid-year $0.50 plus the end of year $0.75 in the bank. This is: $2.25. Better. By compo...