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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
• 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 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

Next Session: Monday, April 12

April 9, 2010             Math 132: Foundations of Mathematics

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