AAA 8.4
SWLT: Use Interest formulas in Installment Buying
Fixed Installment Loans
 Amount Financed:
 The amount a borrower will pay interest on
 Amount Financed = Price of Item – Down Payment
 Total Installment Price:
 The total amount of money the borrow will eventually pay
 Total Installment Price = Sum of All Payments + Down Payment
 Finance Charge:
 The Interest Charged (Money not Percentage) for borrowing
the amount financed.
 Finance Charge = Total Installment Price – Price of Item
Car Loan
 Cat bought a 2-year old Santa Fe
for $12,260. Her down payment
was $3,000 and she will have to
pay $231.50 per month for 4
years.
 Find the amount financed, the
total installment price, and the
finance charge.
 Amount Financed
 Amount Financed =
$12,260 - $3,000
$9,260
 Total Installment Price =
48 x $231.50 + $3,000
$14,112.00
 Finance Charge =
$14,112.00 – $12,260
$1,852
Monthly Payments
 A Young couple bought $9,000
worth of furniture. The down
payment was $1,000. The balance
was financed for 3 years at 8%
simple Interest.
a. Find the Amount Financed
b. Find the Finance Charge
(Interest)
c. Find the total Installment Price
d. Find the Monthly Payment
a. Amount Financed:
$9,000 - $1,000 = $8,000
b. Finance Charge: Simple
Interest Formula
I = $8,000(.08)(3) = $1,920
c.
Total Installment Price
$9,000 + $1,920 = $10,920
d. Monthly Payment
$9,920 ÷ 36 = $275.56
APR
 Many lenders add upfront fees and then spread them out
over the life of the loan, making the actual interest rate
higher than what was quoted
 Because this can be confusing, lenders are required by law
to disclose the annual percentage rate (APR) in a table for
consumers to be able to effectively compare loans
Finding APR
 Step 1: Find the finance charge per $100 borrowed
FinanceCharge
x100
AmountFinanced
 Step 2: Find the row in the table marked with the number of
payments and move to the right until you find the amount closest to
the number in Step 1
 Step 3: The APR (to the nearest half percent) is at the top of the
corresponding column
Burk bought a printer for $600, he made a $50 down
payment and financed the rest for 2 years with monthly
payments of $24.75
 Step 1: Find finance charge per $100
 Total Amount (Not Including Down Payment) = $24.75 x 24 = $594
 Amount Financed = $600 - $50 = $550
 Finance Charge = $594 - $550 = $44
$44
x100 = $8.00
$550
 Step 2: Find row for 24 Payments and move across until you find the
number closest to $8.00
 Step 3: Move to the top, the APR is…
7.5%
Paying loans off early
 Paying loans off early is one way a lender can save
money
 They will avoid paying all of the entire interest,
unearned interest
 There are two methods used to find the unearned
interest:
 The Actuarial Method
 The Rule of 78
The Actuarial Method
kRh
u=
100 + h
 u = Unearned Interest
 k = Number of payments remaining, excluding the current one
 R = Monthly Payment
 h = Finance Charge per $100 for a loan with the same APR (Table 8-1)
and k monthly payments
Using the Actuarial Method
 Burk from slide #7 decides to pay off his laser printer
early, on his 12th payment.
 Find the unearned interest
 Find the payoff amount
Finding the Unearned Interest
(Actuarial Method)
 k = 12
(Half the original payments remain)
 R = $24.75
 h = $4.11
 (The APR is 7.5% and payments
are 12…the intersection of those
rows and columns on the APR
chart is $4.11)
 Formula:
u=
kRh
100 + h
(12)(24.75)(4.11)
u=
100 + 4.11
1, 220.67
u=
»
104.11
11.72
Finding the payoff
 The amount remaining minus the unearned interest.
 13 x $24.75 - $11.72
 = $310.03
The Rule of 78
fk(k +1)
u=
n(n +1)
 u = Unearned Interest
 k = Number of payments remaining, excluding the current one
 f = Finance Charge
 n = Original Number of Payments
Using the Rule of 78
 A $5,000 car loan is to be
paid off in 36 monthly
installments of $172. The
borrower decides to pay the
loan off after 24 payments.
 Total Payments = $172 x 36
$6,192
 Finance Charge =
$6,192 - $5,000 = $1,192
 Substitute into the Formula
 Find the Interest saved
 Find the Payoff amount
 12 x $172 - $139.60 =
$1924.40
fk(k +1) 1,192(12)(12 +1)
u=
=
n(n +1)
36(36 +1)
185, 952
=
»
1,332
$139.60
Computing Credit Card Finance
Charge: Unpaid Balance Method
 Elliot had an unpaid balance of
$365.75 at the beginning of the
month, made purchases of
$436.50, and made a payment of
$200. The interest charged on
the unpaid balance is 1.8% per
month.
 Find the Finance Charge.
 Find the next month’s balance.
 Step 1: Find the Finance Charge on
the unpaid balance using the
simple interest formula.
 I = Prt
 = ($365.75)(0.018)(1)
 = $6.42
 Step 2: New balance = Unpaid
balance + Finance Charge +
Purchases – Payments
 $365.75 + $6.42 + $436.50 – 200
 = $608.67