INSTALLMENT
PURCHASES
CHAPTER 5 – PART 2
INTEREST
CHARGE
BASED ON
REDUCING
BALANCE
Annuity
method
Constant
Ratio
formula
2mI
r
B n  1
CONSTANT
RATIO
FORMULA
CONSTANT
RATIO
FORMULA
2mI
r
B n  1
B n  1r
I 
2m
Example 8.8
A washing machine is being sold for RM2000.
Through an installment purchase, the buyer has to
pay RM400 down payment and 10 monthly
installments. If the interest charged is 8% per
annum on the reducing balance, find the
Total
interest
charged
Monthly
payment
Installment
price
by using the Constant Ratio formula.
Total Interest
Charged
Monthly
Payment
a)
b)
𝐼=
𝐵 𝑛+1 𝑟
2𝑚
𝐼=
1600 10+1 0.08
2(12)
𝑀𝑃 =
𝑀𝑃 =
= 58.67
𝑂𝐵+𝐼
𝑛
1600+58.67
10
= 165.87
Installment
Price
c)
𝐼𝑃 = 𝐶𝑃 + 𝐼
= 2000 + 58.67 = 2058.67
Example 8.10
Rosman purchased a RM4,000 computer. He has to
pay RM1,000 down payment and 20 weekly payments
at RM153 each. Find the approximate effective rate
that is charged by using the Constant Ratio formula.
OB = 4,000 – 1,000 = 3,000
𝑂𝐵 + 𝐼
𝑀𝑃 =
𝑛
3,000 + 𝐼
153 =
20
𝐼 = 153 × 20 − 3,000 = 60
2mI
r
B n  1
2(52)(60)
𝑟=
3,000(20 + 1)
𝑟 = 9.9%

Under the Hire-Purchase Act
(1967), the Rule of 78 is used
to calculate the outstanding
balance of any hire purchase
agreement.

If the consumer decides to
settle the balance of a debt
early, then the lender is not
entitled to all finance charge
in the agreement.
RULE OF 78
1  2  3  ...  N 
B  RN  I 

 1  2  3  ...  n 
 N N  1 
B  RN  I 



n
n

1


RULE OF 78
B = outstanding balance
R = monthly payment
N = number of payments yet to be settled
I = total interest charged
n = total number of payments
 N N  1 
B  RN  I 



n
n

1


 N N  1 
I



n
n

1


Unearned
Interest
Example 8.15
The finance charge on a one-year hire purchase loan is
RM390. Find the interest that was unearned by the
lender if the loan was settled two months early.
 N  N  1 
I

 nn  1 
Unearned
interest
 22  1 
 390 



12
12

1


 15
Example 8.16
A loan of RM10,000 at a flat rate of 10% per annum was repaid by
making 24 monthly installments. Find the
a)
Total interest charged
b)
Monthly payment
c)
Outstanding loan just after the tenth payment using the Rule of
78.
Total interest
I  Pr t
 10,000  10%  2
 2,000
Total interest
Total interest
10,000  2,000
MP 
 500
24
 1414  1 
B  50014   2,000 



24
24

1


 6,300
THE END