# Chapter 9 sec 6 ```Chapter 9 sec 6
How
many of you have bought a car?,
House?, furniture?, RV?, boat?,…
What
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
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.
 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
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