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Consumer Loans

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. Add-On Interest Method. Add-On Interest Method.

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Consumer Loans

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  1. Consumer Loans MATH 102 Contemporary Math S. Rook

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

  3. Add-On Interest Method

  4. Add-On Interest 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:

  5. 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?

  6. 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?

  7. Unpaid Balance Method

  8. 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

  9. 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

  10. 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

  11. 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

  12. Average Daily Balance Method

  13. 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 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

  14. 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

  15. 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

  16. 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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