8 Consumer Mathematics The Mathematics of Everyday Life
Consumer Loans 8.3 • Determine payments for an add-on loan. • Compute finance charges on a credit card using the unpaid balance method.
Consumer Loans 8.3 • Use the average daily balance method to compute credit card charges. • Compare credit card finance charge methods.
The Add-On Interest Method Loans having a fixed number of payments are called closed-ended creditagreements (or installment loans). Each payment is called an installment. The interest charged on a loan is often called a finance charge.
The Add-On Interest Method This method is sometimes called the add-on interest methodbecause we are adding on the interest due on the loan before determining the payments.
The Add-On Interest Method • Example: If you take out an add-on loan for $720 for 2 years at an annual interest rate of 18%, what will be your monthly payments?
The Add-On Interest Method • Example: If you take out an add-on loan for $720 for 2 years at an annual interest rate of 18%, what will be your monthly payments? • Solution:First calculate the interest: • Add interest to the purchase price: • Find the payment:
The Unpaid Balance Method With open-ended credit, you may be making monthly payments on your loan, but you may also be increasing the loan by making further purchases. With the unpaid balance method, the interest is based on the previous month’s balance.
The Unpaid Balance Method • Example: The annual interest rate on a credit card is 18% and the unpaid balance at the beginning of last month was $600. Since then, a purchase of $130 and a payment of $170 were made. • Using the unpaid balance method, what is the credit card bill this month? What is the finance charge next month? (continued on next slide)
The Unpaid Balance Method • Solution: • Previous month’s balance: $600 • Finance charge on last month’s balance: • Purchases made: $130 • Returns: $0 • Payment: $170 (continued onnext slide) Section 9.3, Slide 11
The Unpaid Balance Method Amount owed: Finance charge for next month:
The Unpaid Balance Method • Example: A credit card debt of $6,589 will be paid by making the minimum payment of $100 a month. What will the balance be at the end of 1 month? The annual interest rate on the card is 18%, and the credit card company is using the unpaid balance method to compute the finance charges. (continued on next slide)
The Unpaid Balance Method • Solution: • Unpaid balance: 6,589 – 100 = $6,489 • Amount owed: • Your $100 payment has reduced your debt by only 6,589 – 6,586.34 = $2.66.
The Average Daily Balance Method In the average daily balance method, the balance is the average of all daily balances for the previous month.
The Average Daily Balance Method • Example: At the beginning of September a credit card has a balance of $240. The card has an annual interest rate of 18%, and during September the following adjustments were made on the account: • September 11: payment - $60 credit • September 18: charge - $24 iTune downloads • September 23: charge - $12 gasoline. • Use the average daily balance method to compute the finance charge that will appear on the next statement. (continued on next slide)
The Average Daily Balance Method • Solution: Create a day-by-day record of what is owed the credit card company for each day in September. (continued on next slide)
The Average Daily Balance Method Average daily balance: We see that P= 213.60, r= 0.18, and t =
Comparing Financing Methods • Example: At the beginning of May a credit card has a balance of $500. The annual interest rate is 21%. On May 11, a purchase of $400 (car repair) was made, and on May 29, a payment of $500 was credited. Calculate the finance charge that will appear on the statement for next month using the two methods discussed in this section. (continued on next slide)
Comparing Financing Methods • Solution: unpaid balance method - $7.15 average daily balance method - $12.89