Interest that is compounded more frequently than once each year increases the actual amount earned for the same basic annual rate. If you deposit a certain amount of money in an account where the interest is computed and applied at the end of one year, then you would just receive that full amount earned according to the simple interest formula. If it is computed and applied twice a year, then you would get half of the interest at the six month time, and the other half at the end of the year; however, the amount earned for the second six months uses not just the original principal but includes the interest earned during the first half of the year so is a little higher. The net effect is that you earn half of what you would originally during the first six months and a little more than half during the last six months.

The table gives the effective interest rate (in percent) for several different compounding periods. The basic annual percentage rate (apr) is given in the left-most column. The effective interest rate for the number of compounding periods per year are given in the remaining columns. Another way to interpret the table is to read the numbers as the amount earned in dollars at the end of one year on an initial investment of $100.00.

As an example, if you invest $100.00 in a savings account at 5% apr, then at the end of one year you would receive:

	annual compounding	$5.00	for an effective rate of 5.000%
	semi-annual compounding	$5.06	for an effective rate of 5.063%—this comes from $2.50 that is earned during the first half year (5%/2 of $100.00) and the $2.56 earned during the second half (5%/2 of $102.50)
	monthly compounding	$5.12	for an effective rate of 5.116%
	daily compounding	$5.13	for an effective rate of 5.127%

As can be noted, compounding more often than monthly gains very little in the total earned. Indeed, compounding daily does not even change the basic annual percentage rate very much as compared to weekly or monthly. However, there is another advantage. You do not lose so much when you make a withdrawal early. This is because the interest is computed and applied to your account at more frequent intervals. As an example, if you withdrew the $100.00 one day before the end of the year, you would actually earn:

	annual compounding	$0.00	since the funds were not deposited for the entire year
	semi-annual compounding	$2.50	since you would earn the interest for only the first six months; that is, you would lose the interest for the last portion of the year only (5%/2 on $102.50 or $2.56)
	monthly compounding	$4.68	you would earn interest for the first eleven months, losing only the interest ($0.44) for the last month.
	daily compounding	$5.11	this is the interest earned for the 364 days--you lose only the last day's interest of $0.01

Clearly, when the interest rate is computed and applied daily you gain more flexibility as to when you can deposit and withdraw the funds yet still earn as much as possible.