618 CHAPTER 10 Consumer Mathematics Our next example demonstrates using the installment payment formula to calculate a monthly payment. Example 3 Using the Installment Payment Formula Reread Example 2. Use the installment payment formula to determine Kristin’s monthly payment. Solution In this example, Kristin is borrowing $1500, so p 1500; = the APR is 6%, so r 0.06; = she is making monthly payments, so n 12; = and the time of the loan is 24 months, so the time in years is t 2. 24 12 = = We substitute these values into the installment payment formula. m p r n r n 1 1 1500 0.06 12 1 1 0.06 12 1500(0.005) 1 (1.005) 7.5 1 0.88718567 7.5 0.11281433 66.48 n t ( ) ( 12 2) 24 = ⎛ ⎝ ⎞ ⎠ − ⎛ + ⎝ ⎞ ⎠ = ⎛ ⎝ ⎞ ⎠ − ⎛ + ⎝ ⎞ ⎠ = − ≈ − ≈ ≈ − ⋅ − ⋅ − Thus, Kristin’s monthly payment would be $66.48. Note this matches the payment calculated in Example 2. 7 Now try Exercise 15 Examples 2 and 3 show that either Table 10.2 or the installment payment formula can be used to calculate a monthly payment for an installment loan. The formula has the advantage that it can be used for any APR and any number of payments, not just those given in Table 10.2. One disadvantage of the formula is that if we are given certain information about a loan and we wish to determine the APR, the calculations are beyond the scope of this textbook. For this reason, we will use Table 10.2 in Example 4 to show how to determine the APR on an installment loan. MATHEMATICS TODAY Rent-to-Own Transactions Rent-to-own retailers allow customers to rent furniture, appliances, and electronics over a period of time and, at a specific date, obtain ownership of the item. Customers do not have to submit to a credit check, and the item can be returned at any time. Whether or not these transactions are considered examples of installment buying depends on the state in which the retailer is located. The controversy centers on the total cost of the item if a customer obtains ownership through the rentto-own transaction. A Federal Trade Commission survey found that such purchases cost the customer two to five times as much as similar installment purchases made through other retailers. Why This Is Important Understanding the total price to obtain merchandise is very important when making decisions about purchases. It is usually much more beneficial, if purchasing merchandise, to seek other means than rent-to-own transactions to finance the purchase. TECHNOLOGY TIP Scientific Calculator In Example 3 we determined the monthly payment by evaluating the following expression: 1500 0.06 12 1 1 0.06 12 ( 12 2) ⎛ ⎝⎜ ⎞ ⎠⎟ − + ⎛ ⎝⎜ ⎞ ⎠⎟ − ⋅ There are various ways to evaluate this expression on a scientific calculator. One method is to press the following sequence of keys. ÷ ÷ − + ÷ − × = y ( 1500 ( 0.06 12 ) ) (1 (1 0.06 12) ( ( ) 12 2 ) ) x After the = key is pressed, the answer 66.48091538 is displayed. Eclipse Production/ Shutterstock
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