5/1/2014. Section 8.4 Installment Buying. Installment Buying. Fixed Installment Loans. Objectives

Transcription

1 Section 8.4 Installment Buying Objectives 1. Determine the amount financed, the installment price, and the finance charge for a fixed loan. 2. Determine the APR. 3. Compute unearned interest and the payoff amount for a loan paid off early. 4. Find the interest, the balance due, and the minimum monthly payment for credit card loans. 5. Calculate interest on credit cards using three methods. 5/1/2014 Section Installment Buying Installment Buying: you repay a loan for the cost of a product on a monthly basis Installment Loan: a loan that you pay off with weekly or monthly payments or payment in some other time period. 5/1/2014 Section The amount financed is what the consumer borrows: Amount financed = cash price down payment. The total installment price is the sum of all monthly payments plus the down payment: Total Installment Price = Total of all monthly payments + down payment. The finance charge is the interest on the installment loan: Finance charge = Total installment price - Cash price. 5/1/2014 Section

2 Example: The cost of a used pick-up truck is $9345. We can finance the truck by paying $300 down and $ per month for 60 months. a. Determine the amount financed. b. Determine the total installment price. c. Determine the finance charge. 5/1/2014 Section Solution: Amount financed = cash price down payment = $ $300 = $9045 The amount financed is $9045. b. Total Installment Price = Total of all monthly payments + down payment = $ x 60 + $300 = $11, $300 = $11, The total installment price is $11, /1/2014 Section c. Finance charge = Total installment price - Cash price = $11, $9345 = $ The finance charge for the loan is $ /1/2014 Section

3 : the interest rate per year When comparing two or more loans with different terms, the loan with the lowest APR is the one that charges the least interest 5/1/2014 Section APR Steps in using the APR table below: 1. Compute the finance charge per $100 financed: Finance charge Amount financed $ Look in the row (in table below) corresponding to the number of payments to be made and find the entry closest to the value in step Find the APR at the top of the column in which the entry from step 2 is found. This is the APR rounded to the nearest ½%. 5/1/2014 Section APR Table 5/1/2014 Section

4 APR Example: In the previous example, we found that the amount financed for the truck was $9045 and the finance charge was $ The borrower financed the truck with 60 monthly payments. Use the table to determine the APR. 5/1/2014 Section Solution: Step 1. Find the finance charge per $100 of the amount financed. This means that the borrower pays $28.94 interest for each $100 being financed. Step 2. Use the table to find the number of monthly payments in the first column. Then find the finance charge closest to the value calculated in step #1. The percent heading of the column will be the APR. So the APR is 10.5% 5/1/2014 Section Using a credit card is an example of an open-end installment loan, commonly called revolving credit. Customers receive a statement, called an itemized billing. One method for calculating interest on credit cards is the unpaid balance method. 5/1/2014 Section

5 Example: A particular VISA card calculates interest using the unpaid balance method. The monthly interest rate is 1.3% on the unpaid balance on the first day of the billing period less payments and credits. Here are some of the details in the May 1 May 31 itemized billing: May 1 Unpaid Balance: $1350 Payment Received May 8: $250 Purchases Charged to the VISA Account: Airline tickets: $375, Books: $57, Meals: $65 Last Day of the Billing Period: May 31 Payment Due Date: June 9 5/1/2014 Section a. Find the interest due on the payment due date. b. Find the total balance owed on the last day of the billing period. c. This credit card requires a $10 minimum monthly payment if the total balance owed on the last day of the billing period is less than $360. Otherwise, the minimum monthly payment is 1 36 of the balance owed on the last day of the billing period, rounded to the nearest whole dollar. What is the minimum monthly payment due by June 9? 5/1/2014 Section Solution: a. The monthly interest rate is 1.3% on the unpaid balance on the first day of the billing period, $1350, less payments and credits, $250. The interest due is computed using I = Prt. The interest due on the payment due date is $ /1/2014 Section

6 b. The total balance owed on the last day of the billing cycle is determined as follows: The total balance owed on the last day of the billing period is $ /1/2014 Section c. Because the balance owed on the last day of the billing period, $ , exceeds $360, the customer must pay a minimum of 1 36 of the balance owed. Minimum monthly payment = balance owed $ = $ Rounded to the nearest whole dollar, the minimum monthly payment due by June 9 is $45. 5/1/2014 Section For both methods, I = Prt, where r is the monthly rate and t is one month. Unpaid balance method: The principal, P, is the balance on the first day of the billing period less payments and credits. Previous balance method: The principal, P, is the unpaid balance on the first day of the billing period. 5/1/2014 Section

7 Example: A credit card has a monthly rate of 1.75%. In the January 1-31 itemized billing, the January 1 unpaid balance is $2500. A payment of $1000 was received on January 8. There are no purchases or cash advances in this billing period. The payment due date is February 9. Find the interest due on this date using each of the three methods for calculating credit card interest. Solution: Because the monthly rate is 1.75%, for all three methods I = Prt = P x x 1 month. The principal, P, is different for each method. 5/1/2014 Section a. The Unpaid Balance Method The principal, P, is the unpaid balance on the first day of the billing period, $2500, less payments and credits, $1000. The interest is I= Prt= ($ $1000) x x 1 = $1500 x x 1 = $ The interest due on the payment due date is $ /1/2014 Section b. The Previous Balance Method The principal, P, is the unpaid balance on the first day of the billing period, $2500. The interest is I = Prt = $2500 x x 1 = $ The interest due on the payment due date is $ /1/2014 Section