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Consumer Loans MATH 102 Contemporary Math S. Rook

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Overview Section 9.3 in the textbook: – Add-on interest method – Unpaid balance method – Average daily balance method

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Add-On Interest Method

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Installment loans: loans having a predetermined number of monthly payments n – Also called closed-ended credit agreements because the interest owed is computed at the time of purchase and added on to the loan amount To calculate the monthly payment: – Compute the total of what is owed (P + I) and then divide by n:

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Add-On Interest Method (Example) Ex 1: Luis took out an add-on interest loan for $1,280 to buy a new laptop computer. The loan will be paid back in 2 years and the annual interest rate is 9.5%. a) How much interest will he pay? b) What are his monthly payments?

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Add-On Interest Method (Example) Ex 2: Ben is buying a new boat for $11,000. The dealer is charging him an annual interest rate of 9.2% and is using the add-on method to compute his monthly payments. a)If Ben pays off the boat in 48 months, what are his monthly payments? b)If he makes a down payment of $2,000, what would his new monthly payments be? c)If he wants to have monthly payments of $200, how much should his down payment be?

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Unpaid Balance Method

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Closed-Ended Versus Open-Ended Credit Agreements Recall that installment loans are closed-ended because nothing else affects the amount borrowed once the purchase is made and interest computed With a credit card, the amount borrowed can grow as new purchases are made – i.e. Credit cards are an example of open-ended credit agreements Credit card companies use two common methods to compute payments for borrowers: – Unpaid Balance Method – Average Daily Balance Method

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Unpaid Balance Method Given a previous balance and the interest rate, we use the unpaid balance method to compute a credit card bill as follows: – All purchases for the month are added to the previous balance – All credits for the month are then subtracted from this amount e.g. returns and payments – Resulting amount is known as the unpaid balance

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Unpaid Balance Method (Continued) – A finance charge is computed by applying the interest rate on the unpaid balance for a month Calculated using simple interest I = Prt Recall that in the simple interest formula t is in years – What would the value of t be to represent a month? – The new bill then is computed by adding the finance charge to the unpaid balance

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Unpaid Balance Method (Example) Ex 3: Use the unpaid balance method to i) find the finance charge ii) find the new balance a)Last month’s balance, $475; payment, $225; interest rate, 18%; bought ski jacket, $180; returned camera $145. b)Last month’s balance, $700; payment, $300; interest rate 21%; bought plane ticket $140; bought luggage, $135; paid hotel bill $175

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Average Daily Balance Method

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More complicated calculation, but one often utilized by credit card companies – Hinges on finding the average balance for a month Easiest way to keep track of the balance through a month is to use a table such as done for Example 4 on pages 417-8 in the textbook: – Find the balance on each day of the month and divide the total by the number of days in the month – Involves what is called a weighted average

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Average Daily Balance Method (Continued) The finance charge is then computed using simple interest – The value of t is again 1 ⁄ 12 for one month The new balance will be the finance charge added to the average daily balance

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Average Daily Balance Method (Example) Ex 4: Use the average daily balance method to i) find the finance charge ii) find the new balance: a) August (31 days); previous month’s balance, $280; August 5 th, made payment of $75; August 15 th, charged $135; August 21 st, charged $16; August 24 th, charged $26 b)April (30 days); previous month’s balance, $240; April 3 rd, charged $135; April 13 th, made payment of $150; April 23 rd, charged $30; April 28 th, charged $28

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Summary After studying these slides, you should know how to do the following: – Perform calculations with loans using the: Add-on interest method Unpaid balance method Average daily balance method Additional Practice: – See problems in Section 9.3 Next Lesson: – Annuities (Section 9.4)

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