Math 102 Mathematician: 11.4 Installment Buying ‐ Day 2 Installment Buying Day 1 – Calculate Monthly Payments & Finance Charge Installment Buying Day 2 – Early Repayment of a Loan Installment Buying Day 3 – Credit Card Minimum Monthly Payments Comp Lab Questions 1 – 5, 10 Comp Lab Questions 6 Comp Lab Questions 7 ‐ 9 EARLY REPAYMENT OF A LOAN Example 1 Richie Rich has a 48‐month installment loan with a fixed monthly payment of $83.81. The amount he borrowed was $3500. Instead of making his 18th payment, Richie Rich is paying the remaining balance on the loan. A) Determine the APR of the installment loan. Table Value for Finance Charge = APR = _________% B) Finance Ch arg e
 100  Amount Borrowed
How much interest will Richie save by paying off the loan early? Actuarial Method ‐ Unearned Interest Formula Variables u = n  P V
u
n = 100 V
P = V = C) What is the total amount due to pay off the loan? Total Due = Remaining 30 Payments – Interest Saved + 18th Payment Example 2 Alana took out a 48‐month fixed installment loan for $12,000 to purchase a used SUV. She paid no money down and began making monthly payments of $276.35. Before making her 24th payment, she decides to pay off the loan. A) Determine the APR of the installment loan. B) How much interest will Alana save by paying off the loan early? (Use the actuarial method) C) What is the total amount due to pay off the loan? Math 102 11.4 Installment Buying ‐ Day 3 Mathematician: CREDIT CARD MINIMUM MONTHLY PAYMENTS Minimum Payments – With NO new interest Minimum Monthly Payment = p  r t Months Months NOTE: Always rounded up to the nearest dollar. Minimum Payments – With new interest New outstanding interest principal Minimum Monthly Payment = p  r t + p  r t daily monthly Example 1 – Credit Card Minimum Monthly Payments Faith’s credit card company determines her minimum monthly payment by adding any new interest owed to 2.5% of the outstanding principal. The credit card company charges an interest rate of 0.0385% per day. For Prom, Faith used her credit card on March 18th to purchase her $500 dress and shoes. She made no other purchases in March. Use the given information and the rule that minimum monthly payments are rounded up to the nearest dollar to answer parts a and b below. A) Assuming Faith had no new interest, determine her minimum monthly payment due on April 1, her billing date. The minimum monthly payment due on April 1st is . (rounded up to nearest dollar) B) On April 1, instead of making the minimum payment, Faith makes a payment of $300. Assuming there are no additional charges or cash advances, determine Faith’s minimum payment due on May 1. The minimum monthly payment due on May 1st is . (rounded up to nearest dollar) Example 2 – Credit Card Finance Charge On April 2 billing date, Kianna had a balance of $975.46 on her credit card. From April 2 through May 2, Kianna charged an additional $224.05 and made a payment of $600. A) Find the finance charge on May 2, using the previous balance method. Assume that the interest rate is 1.8% per month. B) Find the new balance on May 2. Example 3 – Credit Card Average Daily Balance The balance on Pierre’s credit card on January 13, his billing date, was $436.09. For the period ending February 13, Pierre had the following transactions. January 20 Charge: Target $78.42 January 28 Payment $200 February 5 Charge: Chipotle $25.17 February 11 Charge: Best Buy $123.15 A) Find the average daily balance for the billing period. B) Find the finance charge to be paid on February 13th. Assume an interest rate of 1.4% per month. C) Find the balance due on February 13th.