Consumer Loans
MATH 102
Contemporary Math
S. Rook
Overview
• Section 9.3 in the textbook:
– Add-on interest method
– Unpaid balance method
– Average daily balance method
Add-On Interest Method
Add-On Interest Method
• Installment loans: loans having a
predetermined number of monthly payments
n
– Also called closed-ended credit agreements
because the interest owed is computed at the time
of purchase and added on to the loan amount
• To calculate the monthly payment:
– Compute the total of what is owed (P + I) and then
divide by n:
PI
monthly payment 
n
Add-On Interest Method (Example)
Ex 1: Luis took out an add-on interest loan for
$1,280 to buy a new laptop computer. The
loan will be paid back in 2 years and the
annual interest rate is 9.5%.
a) How much interest will he pay?
b) What are his monthly payments?
Add-On Interest Method (Example)
Ex 2: Ben is buying a new boat for $11,000. The
dealer is charging him an annual interest rate of 9.2%
and is using the add-on method to compute his
monthly payments.
a) If Ben pays off the boat in 48 months, what are
his monthly payments?
b) If he makes a down payment of $2,000, what
would his new monthly payments be?
c) If he wants to have monthly payments of $200,
how much should his down payment be?
Unpaid Balance Method
Closed-Ended Versus Open-Ended
Credit Agreements
• Recall that installment loans are closed-ended
because nothing else affects the amount borrowed
once the purchase is made and interest computed
• With a credit card, the amount borrowed can grow
as new purchases are made
– i.e. Credit cards are an example of open-ended credit
agreements
• Credit card companies use two common methods to
compute payments for borrowers:
– Unpaid Balance Method
– Average Daily Balance Method
Unpaid Balance Method
• Given a previous balance and the interest rate,
we use the unpaid balance method to compute a
credit card bill as follows:
– All purchases for the month are added to the
previous balance
– All credits for the month are then subtracted from
this amount
• e.g. returns and payments
– Resulting amount is known as the unpaid balance
Unpaid Balance Method
(Continued)
– A finance charge is computed by applying the
interest rate on the unpaid balance for a month
• Calculated using simple interest
I = Prt
• Recall that in the simple interest formula t is in years
– What would the value of t be to represent a month?
– The new bill then is computed by adding the
finance charge to the unpaid balance
Unpaid Balance Method (Example)
Ex 3: Use the unpaid balance method to i) find
the finance charge ii) find the new balance
a) Last month’s balance, $475; payment, $225;
interest rate, 18%; bought ski jacket, $180; returned
camera $145.
b) Last month’s balance, $700; payment, $300;
interest rate 21%; bought plane ticket $140; bought
luggage, $135; paid hotel bill $175
Average Daily Balance Method
Average Daily Balance Method
• More complicated calculation, but one often
utilized by credit card companies
– Hinges on finding the average balance for a month
• Easiest way to keep track of the balance
through a month is to use a table such as done
for Example 4 on pages 417-8 in the textbook:
– Find the balance on each day of the month and
divide the total by the number of days in the
month
– Involves what is called a weighted average
Average Daily Balance Method
(Continued)
• The finance charge is then computed using
simple interest
– The value of t is again 1⁄12 for one month
• The new balance will be the finance charge
added to the average daily balance
Average Daily Balance Method
(Example)
Ex 4: Use the average daily balance method to i) find
the finance charge ii) find the new balance:
a) August (31 days); previous month’s balance, $280;
August 5th, made payment of $75; August 15th,
charged $135; August 21st, charged $16; August 24th,
charged $26
b) April (30 days); previous month’s balance, $240;
April 3rd, charged $135; April 13th, made payment of
$150; April 23rd, charged $30; April 28th, charged $28
Summary
• After studying these slides, you should know
how to do the following:
– Perform calculations with loans using the:
• Add-on interest method
• Unpaid balance method
• Average daily balance method
• Additional Practice:
– See problems in Section 9.3
• Next Lesson:
– Annuities (Section 9.4)