1. THE NATURE OF FINANCIAL MANAGEMENT Copyright © Cengage Learning. All rights reserved. 11

2. Copyright © Cengage Learning. All rights reserved. 11.2 Installment Buying

3. 3 Two types of consumer credit allow you to make installment purchases. The first, called closed-end, is the traditional installment loan. An installment loan is an agreement to pay off a loan or a purchase by making equal payments at regular intervals for some specific period of time. There are two common ways of calculating installment interest. The first uses simple interest and is called add-on interest, and the second uses compound interest and is called amortization.

4. 4 Installment Buying In addition to closed-end credit, it is common to obtain a type of consumer credit called open-end, revolving credit, or, more commonly, a credit card loan. MasterCard, VISA, and Discover cards, as well as those from department stores and oil companies, are examples of open-end loans. This type of loan allows for purchases or cash advances up to a specified maximum line of credit and has a flexible repayment schedule.

5. 5 Add-On Interest

6. 6 The most common method for calculating interest on installment loans is by a method known as add-on interest. It is nothing more than an application of the simple interest formula. It is called add-on interest because the interest is added to the amount borrowed so that both interest and the amount borrowed are paid for over the length of the loan.

7. 7 Add-On Interest You should be familiar with the following variables: P = AMOUNT TO BE FINANCED (present value) r = ADD-ON INTEREST RATE t = TIME (in years) TO REPAY THE LOAN I = AMOUNT OF INTEREST A = AMOUNT TO BE REPAID (future value) m = AMOUNT OF THE MONTHLY PAYMENT N = NUMBER OF PAYMENTS

8. 8 Add-On Interest

9. 9 Example 1 – Find a monthly payment You want to purchase a computer that has a price of $1,399, and you decide to pay for it with installments over 3 years. The store tells you that the interest rate is 15%. What is the amount of each monthly payment? Solution: You ask the clerk how the interest is calculated, and you are told that the store uses add-on interest. Thus, P = 1,399, r = 0.15, t = 13, and N = 36.

10. 10 Example 1 – Solution Two-step solution I = Prt = 1,399(0.15)(3) = 629.55 A = P + I = 1,399 + 629.55 = 2,028.55 cont’d

11. 11 Example 1 – Solution One-step solution A = P(1 + rt) = 1,399(1 + 0.15  3) = 2,028.55 The amount of each monthly payment is $56.35. cont’d

12. 12 Annual Percentage Rate (APR)

13. 13 Annual Percentage Rate (APR) Suppose you borrow $2,000 for 2 years with 10% add on-interest. The amount of interest is $2,000  0.10  2 = $400 Now if you pay back $2,000 + $400 at the end of two years, the annual interest rate is 10%. However, if you make a partial payment of $1,200 at the end of the first year and $1,200 at the end of the second year, your total paid back is still the same ($2,400), but you have now paid a higher annual interest rate.

14. 14 Annual Percentage Rate (APR) Take a look at Figure 11.1. Figure 11.1 Interest on a $2,000 two-year loan

15. 15 Annual Percentage Rate (APR) On the left (figure 11.1) we see that the interest on $2,000 is $400. But if you make a partial payment (figure on the right), we see that $200 for the first year is the correct interest, but the remaining $200 interest piled on the remaining balance of $1,000 is 20% interest (not the stated 10%). Note that since you did not owe $2,000 for 2 years, the interest rate, r, necessary to give $400 interest can be calculated using I = Prt: (2,000)r(1) + (1,000)r(1) = 400

16. 16 Annual Percentage Rate (APR) 3,000r = 400 This number, 13.3%, is called the annual percentage rate.

17. 17 Example 3 – Find an APR for a installment purchase In Example 1, we considered the purchase of a computer with a price of $1,399, paid for in installments over 3 years at an add-on rate of 15%. Use the given APR formula (rounded to the nearest tenth of a percent) to approximate the APR. Solution: Knowing the amount of the purchase is not necessary when finding the APR.

18. 18 Example 3 – Solution We need to know only N and r. Since N is the number of payments, we have N = 12(3) = 36, and r is given as 0.15: The APR is approximately 29.2%. cont’d

19. 19 Open-End Credit

20. 20 Open-End Credit The most common type of open-end credit used today involves credit cards issued by VISA, MasterCard, Discover, American Express, department stores, and oil companies. Because you don’t have to apply for credit each time you want to charge an item, this type of credit is very convenient. When comparing the interest rates on loans, you should use the APR.

21. 21 Open-End Credit Earlier, we introduced a formula for add-on interest; but for credit cards, the stated interest rate is the APR. However, the APR on credit cards is often stated as a daily or a monthly rate. For credit cards, we use a 365-day year rather than a 360-day year.

22. 22 Example 6 – Find APR from a given rate Convert the given credit card rate to APR (rounded to the nearest tenth of a percent). a. per month b. Daily rate of 0.05753% Solution: a. Since there are 12 months per year, multiply a monthly rate by 12 to get the APR:

23. 23 Example 6 – Solution b. Multiply the daily rate by 365 to obtain the APR: 0.05753%  365 = 20.99845% Rounded to the nearest tenth, this is equivalent to 21.0% APR. cont’d

24. 24 Open-End Credit Many credit cards charge an annual fee; some charge $1 every billing period the card is used, whereas others are free. These charges affect the APR differently, depending on how much the credit card is used during the year and on the monthly balance. If you always pay your credit card bill in full as soon as you receive it, the card with no yearly fee would obviously be the best for you.

25. 25 Open-End Credit On the other hand, if you use your credit card to stretch out your payments, the APR is more important than the flat fee. For our purposes, we won’t use the yearly fee in our calculations of APR on credit cards. Like annual fees, the interest rates or APRs for credit cards vary greatly. Because VISA and MasterCard are issued by many different banks, the terms can vary greatly even in one locality.

26. 26 Credit Card Interest

27. 27 Credit Card Interest An interest charge added to a consumer account is often called a finance charge. The finance charges can vary greatly even on credit cards that show the same APR, depending on the way the interest is calculated. There are three generally accepted methods for calculating these charges: previous balance, adjusted balance, and average daily balance.

28. 28 Credit Card Interest

29. 29 Example 7 – Contrast methods for calculating credit card interest Calculate the interest on a $1,000 credit card bill that shows an 18% APR, assuming that $50 is sent on January 3 and is recorded on January 10. Contrast the three methods for calculating the interest. Solution: The three methods are the previous balance method, adjusted balance method, and average daily balance method. All three methods use the formula I = Prt.

30. 30 Example 7 – Solution cont’d

31. 31 Credit Card Interest Many credit cards charge no interest if you pay in full within a certain period of time (usually 20 or 30 days). This is called the grace period. On the other hand, if you borrow cash on your credit card, you should know that many credit cards have an additional charge for cash advances—and these can be as high as 4%. This 4% is in addition to the normal finance charges.