# MATH 102 Contemporary Math S. Rook

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MATH 102 Contemporary Math S. Rook
Consumer Loans MATH 102 Contemporary Math S. Rook

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

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:

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?

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?

Unpaid Balance Method

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

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

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

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

Average Daily Balance Method

Average Daily Balance Method
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 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

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

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 5th, made payment of \$75; August 15th, charged \$135; August 21st, charged \$16; August 24th, charged \$26 b) April (30 days); previous month’s balance, \$240; April 3rd, charged \$135; April 13th, made payment of \$150; April 23rd, charged \$30; April 28th, charged \$28

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)