Chapter 9 sec 6
How
many of you have bought a car?,
House?, furniture?, RV?, boat?,…
What
made you decide to buy these
things?
Did
you look for anything special?
• For example, any special deals, bargains?
Lets
say you bought a couch for
$3000(don’t forget the interest)
in 3 yearly payments using an
add-on interest rate of 10%.
What is your true interest rate?
What
is the “true” interest rate? And
what does it mean?
The “true” interest
rate is the called
the annual percentage rate, or APR,
which we will denote by a.
 Using
the add-on from sec 9.2 we can
compute the I = Prt = (3000)(.10)(3) =
$900. Therefore the amount to be
repaid in 3 equal installments is 3000 +
900 = 3900. Divide by 3, $1300 of
which $1000 is being paid by the
principle and $300 is the interest.
Solving the equation;
 300 = (3000)(r)(1)= for r and r = .10.
Therefore your interest is 10%.
 At
the end of the second year, you make
another payment of $1300, of which
$1000 goes to reduce the principle and
$300 is interest. For the 2nd year you have
paid $300 interest for $2000 loan. Solving
the equation 300 = (2000)(r)(1) = .15.
 Therefore in reality, the interest rate on
your loan for the second year is 15%.
Sorry, it
gets worst for you!!
You make a final payment of $1300.
Paid $1000 on the remaining
principle and $300 for the interest.
Solving the equation 300 =
(1000)(r)(1) = .30
Now the interest rate is 30%
You
got robbed!!!!!!
You better be pissed!!!!
BUT
HOLD ON!!!!
The
interest for the first year + interest
for the second year + interest for the
third year = $900.
Using I = Prt, the equation will look
like;
(3000)(a)(1)
+ (2000)(a)(1)
+ (1000)(a)(1) = 900
 Solve
 6000a
a
for a,
= 900
= 0.15.
 Therefore
the APR is 15%. You can check
it if you borrow $3000 for 1 year at 15%
and then $2000 for 1 year at 15% and
then $1000 or 1 year at 15%, the total
interest for the 3 years is $900.
# of
payments
6
12
24
36
48
Finance charge per $100 (APR)
10%
2.94
5.50
10.75
16.16
21.74
 Finding
11%
3.23
6.06
11.86
17.86
24.06
the APR
12%
3.53
6.62
12.98
19.57
26.40
13%
3.83
7.18
14.10
21.30
28.77
14% 15% 16%
4.12 4.42
4.72
7.74 8.31
8.88
15.23 16.37 17.51
23.04 24.80 26.57
31.17 33.59 36.03
 1.
Find the finance charge on the loan if
it is not already given to you.
 2. Determine the finance charge per
$100 on the loan.
 3. use the line of Table that corresponds
to the number of payments to find the
number closest to the amount found in
step 2.
 4. The top of the column containing the
number found is step 3 is the APR.
 In
order to use the table, you must first
know the finance charge on the loan. If
you borrow $780 and pay a finance
charge of $148.20, then the finance
charge per $100 of the amount is given
by
FC
Borrowed
 FC
x100 
148 . 20
780
is the finance charge.
x100  $ 19
Ann
has agreed to pay off a $5000
loan by making 12 monthly
payments. If the total finance charge
on his loan is $410, what is the APR
she is being charged?
410
x100  $ 8 . 20
5000
Ann
is making 12 monthly payments.
Using the table. The closest amount
is $8.31, therefore it is approximate
APR for her loan is 15%.
Nate
is considering buying a car
costing $18,580. The terms of the
sale require a down payment of
$3200 and the rest to be paid off by
making 36 monthly payments of
$310 each. What is the APR will she
be paying on the car financing?
Amount
being finance is the
purchase price minus the down
payment, which is $18,580 - $3200 =
$ 15,380. Because her payment
amount is 36 x 310 = $11,160, this
makes the finance charge equal to
$15,380 - $11,160 = $4220. Using the
table the finance charge is per $100.
4220
x100  $ 27 . 44
15 ,380
 Now
look at the row of 36 payments. The
APR for this car is approximately a little
over 16%.
Therefore
knowing your APR
is important.