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 February 11th, 2013, 03:24 AM #1 Newbie   Joined: Feb 2013 Posts: 1 Thanks: 0 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?
 February 11th, 2013, 05:11 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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.
 February 11th, 2013, 08:17 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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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# a business permits its customers to pay with a credit card or to receive a percentage discount r for 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 p

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