   SEARCH HOME Math Central Quandaries & Queries  Subject: interest Name: Kimberly Who are you: Parent If I put $2000 in a savings account with 5.05% APR and the interest is compounded daily, but credited monthly, how much would I have at the end of a year? Hi Kimberly. The 5.05% is the annual percentage rate. So each day, you earn 5.05%/365 = 0.013836% interest on your balance. That means that you multiply the previous balance by 1+0.00013836 to get the new balance. The first balance is the principal:$2000

Balance at end of day 1: $2000 * 1.0001386 Balance at end of day 2: ($2000 * 1.0001386) * 1.0001386
Balance at end of day 3: (($2000 * 1.0001386) * 1.0001386) * 1.0001386 and so on... Balance at end of day 365 (one year) is:$2000 * (1.0001386365) = \$2103.77

In fact, you can see that this gives us the general formula for compound interest:
If B = the balance at the end and
P = the principal at the beginning and
R = the APR interest rate and
T = the number of years and
F = the number of times per year that the interest is compounded then

B = P * (1 + R/F)T*F

Notice that when the value is credited to your account doesn't factor into what you earn.

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.