Mastering Installment Loans & APR Calculation for Samsung 50” TV

1. Activity 8 - 5 Buy Now, Pay Later Samsung 50” 1080p Plasma TV, $1299 retail

2. Objectives • Determine the amount financed, the installment price, and the finance charge of an installment loan • Determine the installment payment • Determine the annual percentage rate (APR) using the APR formula and using a table • Determine the unearned interest on a loan if paid before it is due • Determine the interest on a credit card account using the average daily balance method

3. Vocabulary • Closed-end Installment Loan – loan of a fixed amount of money paid off over a fixed amount of time; house and car loans • Installment Price – the total amount paid • Finance charge – the total amount of money that the borrow must pay for the privilege of using the loaner’s money; calculated by the sum of the monthly payment minus the amount borrowed • APR – the annual percentage rate or true interest rate charged • Truth-in-Lending Act – required lenders to provide the borrower with the finance charge and the APR of the loan upfront • Actuarial Method – a method used to determine the unearned interest (if a loan is paid off early) • Open-end Installment loan – variable monthly payments depending on the amount purchased during a period; credit cards • Average daily balance method – method for determining interest owed on most credit cards

4. Activity Significant price cuts have recently take place in the cost of HD televisions. You have decided that now is the time to take the plunge. After researching the features of different types of HD TVs, including LCD, plasma, rear-projection, and picture tube, you have selected a 50 inch HD plasma TV at a cost of $4000. The electronics store salesperson informs you that the store is offering a 36 month installment plan to finance the TV. You are interested and discuss the details with the salesperson.

5. Closed-End Installment Loans In a closed-end installment loan you repay the amount borrowed plus interest in equal payments (usually monthly) over a certain period of time. Such loans are commonly used to purchase furniture, appliances and computers. The length of the loans can vary from a few months to several years.

6. Activity cont The store requires no down payment. The salesperson tells you that can finance the HD plasma TV with 36 monthly payments of $132.46. • Determine the total amount paid • Determine the interest (finance charge) on the loan 36 (132.46) = $4782.96 $4782.96 – $4000 = 782.96 (interest charged)

7. Annual Percentage Rate (APR) • The true annual interest rate charged is called the APR. It can be calculated by the following formula: • In 1969, congress passed the Truth in Lending Act that requires the lender to provide the borrower with the finance change and APR of the loan. The Federal Reserve Board’s web site has very useful information including APR tables like 8.1 in our book. 72i APR = -------------------------------- 3P(n + 1) + i(n – 1) where i = interest rate on the loan P = principal (amount borrowed) n = number of months of the loan

8. Activity cont The store requires no down payment. The salesperson tells you that can finance the HD plasma TV with 36 monthly payments of $132.46. Your total finance charge was $782.96; figure out the APR on your loan. 72i APR = -------------------------------- 3P(n + 1) + i(n – 1) 72(782.96) 56,373.12 = -------------------------------------------- = ----------------- 3(4000)(36+1) + 782.96 (36 – 1) 471,403.60 = 0.1196 or about 12%

9. Competition Suppose a salesperson at a competing electronics store offers the same model 50 inch plasma TV, but at a lower price of $3800. With no down payment required, you can borrow $3800 at 14% APR for 32 months. Whose deal is better? 142.98 775.20 $4572.20

10. Paying Off Loans Early Suppose you got a bonus at work and decided to pay off you HD TV loan early. Would you have to pay the total finance charge of $775.20? At the time of the loan pay off, the lender must return any unearned interest that is saved by paying off the loan early. The most commonly used method to determine the unearned interest is the actuarial method. NO! npv u = ------------ 100 + v Where u = unearned interest n = number of remaining monthly payments p = monthly payment v = value from APR table (n, APR)

11. Activity - Finished Recall that your monthly payment for the 32-month loan from the second store was $142.98 per month. You have paid 20 payments so far. • How many payments remain? • Determine the value v from the APR table • Determine the unearned interest, u, from the formula: • Determine the total amount due to pay off the loan 32 – 20 = 12 7.74 npv 12(142.98)(7.74) u = ------------ = -------------------------- = $123.26 100 + v 100 + 7.74 Amount Left – unearned interest = buy-out price 12(142.98) – 123.26 = $1592.50

12. Open-end Installment Loans Credit cards are a common example of open-end installment loans. There is generally no specific period of time to pay off the loan and you can actually borrow additional monies to purchase merchandise while you still have unpaid loans in the account. Interest in these types of loans are generally figured on the average daily balance method. In this method, a balance is determine for each day of the billing period and then the total is divided by the number of days in that billing period. This gives an average of all daily balances. Credit cards should be paid off at the end of each billing period; otherwise, people can get in over their head.

13. Summary and Homework • Summary • Close-end installment loans are paid off with a fixed payment for a fixed amount of time • Open-end installment loans are paid off with variable payments each month • Installment payment is the amount paid (including interest) in regular payments • Installment price is down payment plus the sum of the monthly payments • Most credit cards use average daily balance method to determine interest payments • Homework • pg 946 – 947; problems 1-3