Why does my interest charged (on loan) fluctuate from my own calculations?

Question

I just want to know if I am calculating the interest correctly. Or is the interest rate is fluctuating slightly? Its not really that big of a fluctuation (we're looking at a range of 5-10 cents off). I'm mostly just curious as to why this is the case.

Here is a transcription of my May loan statement:

       STATEMENT PERIOD  APR07/16 - MAY05/16 -  29 DAYS
       PREVIOUS BALANCE                                  $14,199.17
APR22  INTERNET TRANSFER                                           $600.00CR
MAY05  LIFE INSURANCE CHARGED                                        $3.32
MAY05  DISABILITY INSURANCE CHARGED                                 $10.39
MAY05  INTEREST CHARGED
       APR07-MAY05@ PRIME  2.700% + 7.400% = 10.100%
       TOTAL INTEREST                                              $111.62
       NEW BALANCE                                       $13,742.50

On the back of my statements they actually state the formula used to calculate interest as:

Interest. Interest is calculated on the daily balance of your account at the end of each day. Interest starts from the date of any withdrawal. Interest is due once a month. (The bank) will automatically debit your account for interest amounts owing on the statement date. Unpaid interest will compound whether or not (the bank) has demanded payment from you or started a legal action against you. The interest rate shown on the front is the rate that applies on the statement date. The rate may, however, have changed (once or more than once) since the last statement date.

Even in a leap year, interest is calculated by multiplying the then outstanding principal amount by the current interest rate in effect at the applicable time, dividing the product by 365 and multiplying the result by the number of days in the payment period during which such current interest rate was chargeable.

These are my calculations:

PRINCIPAL = 14199.17
RATE      = 0.101
TRANSFER  = 600
INTEREST  = PRINCIPAL * RATE / 365 * TIME

INTEREST BEFORE TRANSFER (14 DAYS) = 14199.17 * 0.101 / 365 * 14
                                   = 55.00719556

INTEREST AFTER TRANSFER (15 DAYS)  = (14199.17 + 55.00719556 - 600) * 0.101 / 365 * 15
                                   = 56.67418754

TOTAL INTEREST = 55.00719556 + 56.67418754 
               = 111.6813831

DIFFERENCE     = 111.6813831 - 111.62
               = 0.061383099

Differences

MAY     0.061383099
JUNE    0.103612429
JULY    0.056803384

Answer 1

It seems you are adding the transfer 1 day off - also, there is no compounding of the amounts prior to the transfer, for the period after the transfer. When recalculating the amount as follows, I get the same $111.62 result as the bank:

14199.17 * 0.101 / 365 * 15 + (14199.17 - 600) * 0.101 / 365 * 14

An alternate calculation would be to apply the full month of interest against the balance there the entire 29 days, and then calculate the additional interest on the amount there up to the point of transfer:

(14199.17 - 600) * 0.101 / 365 * 29 = 109.13

+

600 * 0.101 / 365 * 15 = 2.49

= 

$111.62