Math CentralQuandaries & 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.

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