8-4 Installment Buying
Installment buying is when an item is purchased and the buyer pays for it by making periodic
partial payments, or installments.
fixed installment loan - a loan that is repaid in equal payments.
down payment – part of the cost you pay at the time of purchase.
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 buyer will ultimately pay.
Total installment price = Sum of all payments + Down payment
finance charge - the interest charged for borrowing the amount financed.
Finance charge = Total installment price – Price of item
Ex: For an automotive loan, find the amount financed, the total installment price, and the
finance charge for the following:
Purchase price: $19,500
sales tax: 6.5%
license and title fees: $375
down payment: $3,500
payments: $390.25 for 60 months
Price of car = purchase price + tax + license and title fees = 19500 + 19500(0.065) + 375 =
$21,142.50
Amount financed = price of item – down payment
Amount financed = (19500 + 19500*0.065 + 375) – 3500
= (19500 + 1267.50) – 3500
= 21,142.50 – 3500
= $17,642.50
Total installment price = Sum of all payments + Down payment
= $390.25(60) + 3,500
= $26,915
Finance charge = Total installment price – Price of item
= $26, 915 - $21,142.50
= $5,772.50
Annual Percentage Rate (APR)
Lenders are required by law to disclose an annual percentage rate, or APR, that reflects the
true interest charged. This allows consumers to compare loans with different terms.
Using the APR Table
1) Find the finance charge per $100 borrowed using the formula
Finance Charge
 $100
Amount Financed
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 from Step 1.
3) The APR (to the nearest half percent) is at the top of the corresponding column.
Ex: Joy bought a new car for $14,400. She made a down payment of $4,000 and made monthly
payments of $319 for 3 years. Find the APR.
1) Finance charge = Total installment price – Price of item
= [$319(36 months) + $4,000] - $14,400
= $1,084
Amount financed = $14,400 - $4,000 = $10,400
Finance ch arg e
1084
 100 
 100  10.42
amount financed
10400
2) 36 payments, finance charge per $100 ≈$10.42
3) 6.5%
Unearned Interest
unearned interest - the amount of the finance charge that is saved when a loan is paid off early
2 methods: The Actuarial Method and The Rule of 78
Actuarial Method
u
kRh
100  h
where 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 and k monthly payments
Ex. Joy bought a new car for $14,400. She made a down payment of $4,000 and made monthly
payments of $319 for 3 years and had an APR of 6.5%. She decided to pay off her loan at the
end of 2 years. Using the actuarial method, find the unearned interest and payoff amount.
k = # of payments, excluding the current one = 36 months – 24 months = 12 months
R = $319
h = $3.56 (APR = 6.5%, k = 12 months, use APR table)
kRh
100  h
12(319)(3.56)
u
100  3.56
13627.68

103.56
 131.59
u
The unearned interest is $131.59.
Payoff amount = number of payments remaining x amount of payment – unearned interest
*Note: number of payments = # remaining + the payment at the end of the second year
Payoff amount = 13(319) – 131.59 = $4,015.41
The Rule of 78
u
fk (k  1)
n(n  1)
u = unearned interest
f = finance charge
k = number of remaining monthly payments
n = original number of payments
Ex. A company borrowed $600 to purchase items from a store that was going out of business.
The loan required 24 monthly payments of $29.50. After 18 payments were made, the
company decided to pay off the loan. How much interest was saved? Use the rule of 78.
f = Total payments – amount financed = ($29.50)(24 months) – 600 = $108
k = # payments left = 6
n = # of original payments = 24
fk (k  1)
n(n  1)
(108)(6)(6  1)
u
24(24  1)
4536

600
 7.56
u
Total unearned interest is $7.56
Credit Cards: The Unpaid Balance Method
Ex: On the first day of Jill’s April credit card billing cycle, her unpaid balance was $678.34. She
then made purchases of $3,479.03. She made a payment of $525.00 during the billing cycle. If
the interest rate is 2.25% per month on the unpaid balance, find the finance charge and the
new balance on the first day of the May billing cycle.
I = Prt (use 1 month for t because interest rate is given per month)
I = (678.34)(0.0225)(1) = 15.26
The interest is $15.26.
New balance = 678.34 + 15.26 + 3479.03 – 525 = 3647.63
The new balance is $3,647.63.
Credit Cards: The Average Daily Balance Method
Procedure for the ADB Method:
Step 1 Find the balance as of each transaction.
Step 2 Find the number of days for each balance.
Step 3 Multiply the balances by the number of days and find the sum.
Step 4 Divide the sum by the number of days in the month.
Step 5 Find the finance charge (multiply the average daily balance by the monthly rate).
Step 6 Find the new balance (add the finance charge to the balance as of the last transaction).
Ex. Charlie’s credit card statement showed these transactions during December:
December 1
December 15
December 16
December 22
Previous balance
Purchases
Purchases
Payment
$1,325.65
$287.62
$439.16
$700.00
(a) Find the average daily balance.
(b) Find the finance charge for the month. The interest rate is 2% per month of the average
daily balance.
(c) Find the new balance on January 1.
Step 1:
December 1
December 15
December 16
December 22
Steps 2 and 3:
Date
December 1
December 15
December 16
December 22
$1,325.65
$1,325.65 + $287.62 = $1,613.27
$1,613.27 + $439.16 = $2,052.43
$2,052.43 - $700 = $1,352.43
Balance
$1,325.65
$1,613.27
$2,052.43
$1,352.43
Days
15 – 1 = 14
16 – 15 = 1
22 – 16 = 6
31 – 22 + 1 = 10
31
$46,011.09
 $1,484.23
31
Step 5: Finance charge = $1,484.23(0.02) = $29.68
Step 6: New balance = $1,352.43 + $29.68 = $1,382.11
Step 4: average daily balance =
(a) Find the average daily balance = $1,484.23
(b) Find the finance charge for the month = $29.68
(c) Find the new balance on January 1 = $1,382.11
Calculations
$1,325.65(14) = $18,559.10
$1,613.27(1) = $1,613.27
$2,052.43(6) = $12,314.58
$1,352.43(10) = $13,524.30
$46,011.25