I am trying to fiqure out what the calculation would be when borrowing
money on a precomputed interst basis. The discount is 9.50%/100 per
year of the total note and service charge is total note/50*$1.50. the
loan is to be paid in 12 equal payments.  Example amount given to
customer 500.00 for 12 months. I know the discount or int would be
47.50 and the service charge would be 15.00 but this is on the amount
given to customer, not on the total note which would be amount given
to cust + int +service charge which equals 562.50.  I can not figure
out how to start with the total note to get the interest amount and
service charge.  Thank you for your help

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Request for Question Clarification by elmarto-ga on 04 Sep 2005 20:29 PDT

Hello bubba,
I just want to check if I understood your question correctly before
posting an answer. You would like to know what should the value of the
total note be so that the customer receives $500 plus the int+service
fees (calculated on the total value of the note. Is this correct?

Thanks,
elmarto

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Clarification of Question by bubba15-ga on 05 Sep 2005 06:17 PDT

Dear Sir

I believe you underestand the question.  I know how to calculate the
correct int and ser. cahrge if I am given the total note.  I can not
get what the formaula would be to start at the total note amount to
calculate the correct amount of interest and service charge if I want
the customer to recieve $500.00.  Especially since if I increase the
term of the loan from 12 months to 24 months everything changes, so I
am looking for a formula to use to arrive at the correct calculation.

Thank you

Michael

Hello bubba,
Your question can be answered with a simple mathematical equation.
First let me redefine the "service" fees you mention. If this charge
is $1.50/50*note, then this is the same as $0.03*note. This, in turn,
means that the service charge is 3 cents per dollar; or in other
words, 3% of the total note.

Now, on to the formula. You stated that you want the customer to
borrow money equal to $500 plus the int+service charges on the total
note. So let's call "X" to the value of the total note. If the loans
is for 12 months, then the costs associated with this loan will be:

costs = 9.5% of X  +  3% of X
      = 0.095*X + 0.03*X
      = 0.125*X

Now, if the total note must cover $500 plus its costs, then we have that:

X = $500 + "costs of borrowing X"
X = 500 + 0.125*X

And now we must simply isolate X to get the answer:

X           = 500 + 0.125*X
X - 0.125*X = 500
X*(1-0.125) = 500
X*0.875     = 500
X           = 500/0.875
X           = 571.42 (rounded)

So the value of the total note should be $571.42. Let's verify that
this is correct. If you borrow $571.42, you will have to pay a service
charge of 0.03*571.42 = $17.14; and interests of 0.095*571.42 =
$54.28. Therefore, the total cost of this loan will be 17.14+54.28 =
$71.42. So, as you see, the customer will receive $500 plus the $71.42
needed to cover the costs of the total note.

The formula I provided can be easily adapted to other amounts (instead
of $500) and other interest and service fees. If you need to adapt it
and have any trouble with it, or if there is anything unclear about my
answer, please don't hesitate to request clarification.


I hope this helps!
Best wishes,
elmarto

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Request for Answer Clarification by bubba15-ga on 05 Sep 2005 14:00 PDT

Elmarto,

I first want to thank you for the help, I think you have it correct,
but being a person that is in the consumer loan business, but hates
#'s, perhaps if you could show me how this might look in a program
such as Microsoft Excel, if my customer wants to receive 500.00 with
the same 9.50% discount and service charge of 1.50/50 of the total
note for both a 12 month and 24 month contract.  Again, the discount
is $9.50 per 100 per year of the total note.  Again, thank you for
your response, I just can not make it work in Excell.

Bubba

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Clarification of Answer by elmarto-ga on 05 Sep 2005 14:39 PDT

Hello!
I'm glad you liked my answer. You can find a simple Excel spreadsheet at

http://www.angelfire.com/alt/elmarto/googleanswers/564157loan.xls

You can change the $500 to see what the value of the total note should
be with other amounts. The sheet will give the note values for a
12-month and a 24-month loan.

Best wishes!
elmarto

Elmarto answered my question quickly, precisely and perfectfully. I
could not have asked for anything better.

I am glad that you two seemed to have agreed on the terms, but I don't
see where the 12 regular and equal payments are reflected, which will
reduce the interest amount.
To me, it seems that the problem is confused by speaking of a "note",
which for bankers suggests a one time final settlement of the debt. 
Similarly, the mention of "discount" suggests that the amount due at
final maturity is know and  the amount to be paid is what is being
calculated.

If I understand the problem correctly (which may not be true), the
borrower receives $ 500 and must also finance the $ 15 service charge,
which the lender pockets up-front, so the debt is for $ 515.  Interest
will be calculated at 9.5% per annum, and the loan settled by 12 equal
payments.  Let's assume 12 monthly payments due at the end of each
period, just to be ultra precise.

Then the financial calculation is to determine what amount the 12
equal payments must be at 9.5% interest to settle the loan plus
service charge (= $ 515).
My trusty HP12c calculator tells me that this is $ 45.157 per month, a
total of $ 541.884.
This is less than the $ 571.42 in the answer because the debt is being
reduced each month, reducing the amount on which interest is due in
the subsequent months.

If the same loan is to be repaid over 24 months, the payments would be
$ 23.646, a total of $ 567.50, more than before because the loan would
be outstanding for a longer period of time.

Here is an site with online calculators: 
http://homebuying.about.com/cs/calculators/a/calculators.htm

Click on "what's missing" and then on "what will be my monthly
payment", and then enter the interest rate (9.5), period (1 year), and
amount (515), and hit "calculate".

If I have misunderstood the definition of the problem, please let me know.
Myoarin

Bubba,
Regardless whether my calculation is correct or not, I think someone
in the consumer loan business should have a handle on the numbers. 
You don't have to know how to calculate interest and payments with a
slide rule, but should know how to use software that gives the right
answers.  They are too easy to check these days.  Truth in Lending
Laws can be a nuisance.

Here is another site with some software:

http://www.programurl.com/loan-and-mortgage.htm

Myoarin

Myoarin
For your information, I am quite capable of verifying that interest
charged and service fee charged are correct and in compliance with my
particular state laws.  Your calculation was incorrect due to the
simple fact that the term precompute means that the interest and
service charge are added at the begining and the loan begins with the
total of payments, this is not a simple interest type of product.  I
am not nor do I claim to be a mathmetician, I was simply looking for
help with the formula to arrive at the totals. The consumer finance
business involves way more important things than being able to figure
out a formula, such as the ability to read and understand people,
because it is easy to lend money out, but it takes a unique person
that can get it paid back.  I have been very successful over the past
10 years in this business, and now own 3 independent offices, and I do
have a handle on the numbers.  We are considering a change in software
companies and was simply trying to assist them with the programming of
the formula.

Respectfully

Bubba

My apologies, Bubba, and my congratulations on your success.
I obviously misunderstood that with the terminology you use it is
acceptable to charge interest on an amount plus service charge that is
not received by the customer.

"Therefore, the total cost of this loan will be 17.14+54.28 =
$71.42. So, as you see, the customer will receive $500 plus the $71.42
needed to cover the costs of the total note."   (Elmarto-ga)

I understood that the customer would receive $500, plus owing you $15
service charge.  If he repays you the $571.42 ("total note") in 12
equal monthly payments of $47.62, that represents an interest rate of
19.64% pa.

More congratulations!  Tell me where I went wrong, please.
Myoarin

Thank you very much for the nice comments and tip!