W8D15 Installment Buying

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					   8.2 & 8.3 Homework Solutions
• 459:
35.a. I = (4000)(0.0825)(0.75) = $247.50
   b. $4,247.50

• 465:
1. A = $10,000(1 + 0.04)2 = $10,816
   $816 in interest earned
2. A = $8,000(1 + 0.06)3 = $9,528.13
   $1,528.13 in interest earned
April 9, 2010                    Math 132: Foundations of Mathematics
               Math 132:
       Foundations of Mathematics

                       Amy Lewis
                       Math Specialist
                IU1 Center for STEM Education


April 9, 2010                       Math 132: Foundations of Mathematics
                8.5 Installment Buying
• Determine the amount financed, the
  installment price, and the finance charge
  for a fixed loan.
• Determine the APR.




April 9, 2010                 Math 132: Foundations of Mathematics
                Installment Buying
• Installment buying is when you repay a
  loan for the cost of a product on a monthly
  basis. For example, using a credit card.
• An installment loan is one that you can pay
  off with weekly or monthly payments or
  payments in some other time period. For
  example, a car loan.
• What are the advantages of this kind of a
  loan?
April 9, 2010               Math 132: Foundations of Mathematics
                Fixed Installment Loans
• A loan that has a schedule for paying a fixed
  amount each period.
                  Amount Financed =
              Cash price – Down payment
                Total Installment Price =
   Total of all monthly payments + Down payment
                   Finance Charge =
         Total installment price – Cash price
April 9, 2010                  Math 132: Foundations of Mathematics
                Fixed Installment Loans
• The cost of a new car is $14,000. You can
  finance the car by paying $280 down and
  $315 per month for 60 months.
     – Determine the amount financed.
     – Determine the total installment price.
     – Determine the finance charge.


April 9, 2010                    Math 132: Foundations of Mathematics
                Annual Percentage Rate
• APR is the interest rate per year.
     – The loan with the lowest APR is the one that
       charges the least interest.
     – At what rate did we finance our new car?




April 9, 2010                    Math 132: Foundations of Mathematics
                Annual Percentage Rate
• Steps in using an APR Table
     – Compute the finance charge per $100 financed:
                   Finance charge x $100
                  Amount financed
     – Find the row corresponding to the number of
       payments and find the entry closest to the value in
       step 1.
     – Find the APR at the top of the column in which the
       entry from step 2 is found.

April 9, 2010                              Math 132: Foundations of Mathematics
                Annual Percentage Rate
• Determine the APR for our new car loan.




April 9, 2010                 Math 132: Foundations of Mathematics
    Computing Unearned Interest
• Unearned interest is the amount by which a
  loan’s finance charge is reduced when the loan
  is paid off early.
Actuarial Method
u = unearned interest
k = remaining number of scheduled payments
  (excluding current payment)
R = regular monthly payment
V = finance charge per $100 for a loan with the
  same APR and k monthly payment

April 9, 2010                 Math 132: Foundations of Mathematics
    Computing Unearned Interest
• Instead of making the 24th payment on the
  car loan, we decide to pay the remaining
  balance and terminate the loan.
     – Use the actuarial method to determine how
       much interest will be saved by repaying the
       loan early.
     – Find the payoff amount.
     Current payment + total of remaining payments – interest saved

April 9, 2010                               Math 132: Foundations of Mathematics
                Homework
• 488: 11 & 12
• Work on your project!

Next Session: Monday, April 12




April 9, 2010             Math 132: Foundations of Mathematics

				
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