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AAA 8.4 SWLT: Use Interest formulas in Installment Buying Fixed Installment Loans Amount Financed: The amount a borrower will pay interest on Amount Financed = Price of Item – Down Payment Total Installment Price: The total amount of money the borrow will eventually pay Total Installment Price = Sum of All Payments + Down Payment Finance Charge: The Interest Charged (Money not Percentage) for borrowing the amount financed. Finance Charge = Total Installment Price – Price of Item Car Loan Cat bought a 2-year old Santa Fe for $12,260. Her down payment was $3,000 and she will have to pay $231.50 per month for 4 years. Find the amount financed, the total installment price, and the finance charge. Amount Financed Amount Financed = $12,260 - $3,000 $9,260 Total Installment Price = 48 x $231.50 + $3,000 $14,112.00 Finance Charge = $14,112.00 – $12,260 $1,852 Monthly Payments A Young couple bought $9,000 worth of furniture. The down payment was $1,000. The balance was financed for 3 years at 8% simple Interest. a. Find the Amount Financed b. Find the Finance Charge (Interest) c. Find the total Installment Price d. Find the Monthly Payment a. Amount Financed: $9,000 - $1,000 = $8,000 b. Finance Charge: Simple Interest Formula I = $8,000(.08)(3) = $1,920 c. Total Installment Price $9,000 + $1,920 = $10,920 d. Monthly Payment $9,920 ÷ 36 = $275.56 APR Many lenders add upfront fees and then spread them out over the life of the loan, making the actual interest rate higher than what was quoted Because this can be confusing, lenders are required by law to disclose the annual percentage rate (APR) in a table for consumers to be able to effectively compare loans Finding APR Step 1: Find the finance charge per $100 borrowed FinanceCharge x100 AmountFinanced Step 2: Find the row in the table marked with the number of payments and move to the right until you find the amount closest to the number in Step 1 Step 3: The APR (to the nearest half percent) is at the top of the corresponding column Burk bought a printer for $600, he made a $50 down payment and financed the rest for 2 years with monthly payments of $24.75 Step 1: Find finance charge per $100 Total Amount (Not Including Down Payment) = $24.75 x 24 = $594 Amount Financed = $600 - $50 = $550 Finance Charge = $594 - $550 = $44 $44 x100 = $8.00 $550 Step 2: Find row for 24 Payments and move across until you find the number closest to $8.00 Step 3: Move to the top, the APR is… 7.5% Paying loans off early Paying loans off early is one way a lender can save money They will avoid paying all of the entire interest, unearned interest There are two methods used to find the unearned interest: The Actuarial Method The Rule of 78 The Actuarial Method kRh u= 100 + h u = Unearned Interest k = Number of payments remaining, excluding the current one R = Monthly Payment h = Finance Charge per $100 for a loan with the same APR (Table 8-1) and k monthly payments Using the Actuarial Method Burk from slide #7 decides to pay off his laser printer early, on his 12th payment. Find the unearned interest Find the payoff amount Finding the Unearned Interest (Actuarial Method) k = 12 (Half the original payments remain) R = $24.75 h = $4.11 (The APR is 7.5% and payments are 12…the intersection of those rows and columns on the APR chart is $4.11) Formula: u= kRh 100 + h (12)(24.75)(4.11) u= 100 + 4.11 1, 220.67 u= » 104.11 11.72 Finding the payoff The amount remaining minus the unearned interest. 13 x $24.75 - $11.72 = $310.03 The Rule of 78 fk(k +1) u= n(n +1) u = Unearned Interest k = Number of payments remaining, excluding the current one f = Finance Charge n = Original Number of Payments Using the Rule of 78 A $5,000 car loan is to be paid off in 36 monthly installments of $172. The borrower decides to pay the loan off after 24 payments. Total Payments = $172 x 36 $6,192 Finance Charge = $6,192 - $5,000 = $1,192 Substitute into the Formula Find the Interest saved Find the Payoff amount 12 x $172 - $139.60 = $1924.40 fk(k +1) 1,192(12)(12 +1) u= = n(n +1) 36(36 +1) 185, 952 = » 1,332 $139.60 Computing Credit Card Finance Charge: Unpaid Balance Method Elliot had an unpaid balance of $365.75 at the beginning of the month, made purchases of $436.50, and made a payment of $200. The interest charged on the unpaid balance is 1.8% per month. Find the Finance Charge. Find the next month’s balance. Step 1: Find the Finance Charge on the unpaid balance using the simple interest formula. I = Prt = ($365.75)(0.018)(1) = $6.42 Step 2: New balance = Unpaid balance + Finance Charge + Purchases – Payments $365.75 + $6.42 + $436.50 – 200 = $608.67