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February 11th, 2013, 03:24 AM   #1
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Need help with financial mathematics

Hi guys, I have a question related to financial maths.

A business permits its customers to pay with a credit card or to receive a percentage discount r by paying cash.
For credit card purchases, the business receives 95% of the purchase price one-half month later.
At an effective annual rate of 12%, the two payment methods are equivalent.
Determine r.

What I don't understand here is the purpose of the effective annual rate. Why is it existing in the question?
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February 11th, 2013, 05:11 AM   #2
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Re: Need help with financial mathematics

You are comparing a payment now vs. a payment at the end of the month. When you compare payments at different times you need an interest rate to convert between them.
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February 11th, 2013, 08:17 AM   #3
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Re: Need help with financial mathematics

Code:
MTH    RECEIPT   INTEREST  BALANCE
00                             .00 (sale = $1000.00)
.5      950.00              950.00 (95% received)
12                109.25  1,059.25 (interest for 11.5 months)

00    1,000.00     -r          ?   (sale = 1000.00, discount r = ?)
12                  ?     1,059.25 (interest for 12 months = ?)
EXAMPLE: sale = $1,000.00

Top portion: payment = 95% of sale received 1/2 month later.
12% annual interest to be earned next 11.5 months:
950 * .12 = 114; 114 * 11.5/12 = 109.25 = interest
So future value of $1,000.00 sale on Jan.1 = 1,059.25 1 year later.

If payment received Jan.1 instead, what discount can be allowed
such that result 1 year later is also 1,059.25 ?

1.12(1000 - d) = 1059.25: solve to get discount amount d = 54.25

And we have (bottom portion of above):
Code:
00    1,000.00     -54.25       945.75 (sale = 1000.00, discount = 5.425%)
12                 113.50     1,059.25 (interest for 12 months on 945.75)
So discount rate r = 54.25 / 100 = .5425 or 5.425%
Clear nuff?
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