How do we calculate a loan with daily compoundable interest?

Question

I suppose this might not be strictly a Microsoft Excel subject.  Nevertheless I am helping a friend who is using Excel to store the downloaded data from the bank and trying to calculate the daily balance.  Repayment and withdrawal can be done any
day.
I have figured out a formula as follows but the calculations from the formula doesn't seem to tally with the figures I got from the bank.  I love to hear opinions from anyone who is interested.  There is not always a transaction, i.e. withdrawal
or repayment, every day.  It also takes into account of possible difference of interest rate between two consecutive days.
The formula is owing = (P(1+I/365)^(today date - date of previous transaction) - credit + debit)(1 + I/365) where P is principal and I interest.
G96=(F95*(1+I95/365)^(A96-A95)-D96+C96)*(1+I96/365)
Below is how I try the formula to some data of years ago.
         A                  C               D                 
F                    G                     I
         DATE            DEBIT        CREDIT         OWING            my
calculation  INTEREST
95     23/12/2005                    $650.00        -$52,763.18     -$54,073.49    
6.96% 
96     28/12/2005                    $1,500.00     -$51,263.18     -$54,323.86    
6.96% 
97     3/01/2006     $519.85                         -$51,783.03     -$50,811.70    
6.96% 
98     3/01/2006     $6.50                             -$51,789.53    
-$51,786.40     6.96% 

Answer 1

healee wrote previously:
The formula is owing = (P(1+I/365)^(today date - date of previous transaction) - credit + debit)(1 + I/365) where P is principal and I interest.
G96=(F95*(1+I95/365)^(A96-A95)-D96+C96)*(1+I96/365)
Refer to the file "example modified.xlsx" (click here) [1].  This demonstrates two methods for calculating interest on loans based on the following.
As I noted previously, since you are unable to provide actual bank data that includes interest, there is no way to validate or invalidate the demonstrated methods.  They only serve to clarify the points that I make below.
If loan interest is computed and compounded daily (which would be unusual, IMHO), your formula is almost correct.
One problem is the reference to F95, as I said before.  The correct way to do this is to copy the outstanding balance from a bank statement one time into G2.
The other problem is:  you are double-accounting some interest.  Interest is usually computed based on the account balance at the end of the business day.  All intraday transactions, debits and credits, are netted.
However, it is more common (AFAIK) to charge simple interest on the daily balance or to use an average daily balance for the billing period.
Then a minimum payment -- perhaps interest-only -- is billed at the end of the period.  If the minimum payment is not paid within some grace period (e.g. 15 days),
only then, if at all, is the unpaid interest (and perhaps a penalty) added to the principal, resulting in compounded interest.
Alternatively, even then unpaid interest and penalties are not added to principal and do not compound.  Instead, unpaid interest and penalties might accumulate separately, eventually resulting in closing the account and collecting or writing off the
bad debt.
healee wrote:
According to
http://en.wikipedia.org/wiki/Nominal_interest_rate, in finance and economics, nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation (in contrast with the real interest rate).
And the sentence continues:  ``or,
for interest rates "as stated" without adjustment for the full effect of compounding``.
That is the context in which I meant my comments to be taken. 
The wiki article is divided into two very different sections:  "Nominal versus real interest" and "Nominal versus effective interest rate".
It is the latter that we are talking about.
(If I were a wiki editor, I would spit that article into two in order to "disambiguate" the definitions.)
healee wrote:
I have supposed somebody must know how the banks work in terms of calculating the principal and interest though they might vary with regions.  Is it possible the method could very with banks in the same jurisdiction?
In my experience, bank employees do not understand the mathematical mechanics of the bank's procedures except in general terms.  In any case, generally they are not a reliable source of information.
In the US, banks and lenders are required to provide a "disclosure statement" which does detail some bank procedures.
AFAIK, even in the US, such statements are not
required to explain how interest is calculated.  But the ones that I have studied do.
And yes:  in the US, two banks in the same city block can use different procedures for charging interest on loans.
I believe that banks and lenders are only required to use "reasonable" methods for computing actual interest.
In any case, I do not know anything about Australia banking regulations.  They may be more or less strict.
Healee wrote:
When you say Australia interest rates are reported as a nominal (simple) rate, do you mean they are not calculated as compound interest rates?
No.  How rates are reported can be different from how rates are applied to compute actual interest.  At least, in general.  Again, Australia regulations might dictate something different.
Moreover, my inference that Australia loan rates are reported as nominal (simple) rates is not dispositive.  It is just suggestive.
The importance is how we should "de-annualize" a stated interest rate; that is, compute a sub-annual periodic rate.
But again, how that periodic rate is applied can be something different altogether.
healee wrote:
in fact every rate is compounded.  The difference is only when it is compounded.  If it is compounded weekly for argument's sake, then the interest is calculated at a simple rate daily but calculated at a compound rate at the end
of the weekly cycle.
That might apply to savings interest.  But we are talking about loan interest (or a line of credit) here.
Usually, loan interest charged in a billing period is expected to be paid in full.  So normally, loan interest does not compound from one billing period to another.  (What a bank does with unpaid debt varies widely.)
But that does not tell us how a lender computes intra-period interest.  It can be compounded (typically daily), or it can accrue separately as simple interest.
Some countries might regulate those details.  Others might allow it to vary from bank to bank.
[EDIT] PS:  Another factor that I forgot to mention:  rounding.  Whether or not to round interest and when, especially daily interest, is up to the lender and/or government policies.  I purposely do not round interest calculations. 
But I have seen it done both ways in the US.  I would not sweat the detail until we have some real data to compare to.
[1] http://www.box.com/s/3v9ajtt0e4vs44ar3s3j