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 $ 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 $ $3,000 $14,  Finance Charge = $14, – $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  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  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  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 12 th 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:

Finding the payoff  The amount remaining minus the unearned interest.  13 x $ $11.72  = $310.03

The Rule of 78  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.  Find the Interest saved  Find the Payoff amount  12 x $172 - $ = $  Total Payments = $172 x 36 $6,192  Finance Charge = $6,192 - $5,000 = $1,192  Substitute into the Formula

Computing Credit Card Finance Charge: Unpaid Balance Method  Elliot had an unpaid balance of $ 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  $ $ $ – 200  = $608.67