A newly married couple bought a stove by paying 30 monthly instalments of RM60. The cash price of the stove is RM1,230. However, the couple decides to settle the balance immediately after paying for 2 years. How much should the couple pay using the Rule of 78?
Answer (1)
To solve this problem, we need to use the Rule of 78, which is commonly used for calculating interest rebates on installment loans when they are paid off early. The Rule of 78 gives more of the interest in the earlier payments and less in the later ones.
Let's break down the problem step by step:
Understand the loan details :
Total number of payments: 30
Monthly payment: RM60
Cash price of the stove: RM1,230
Calculate the total amount paid with installments :
Total installments paid = 30 payments * RM60 = RM1,800
So, the total interest paid = RM1,800 (installment total) - RM1,230 (cash price) = RM570
Determine how many payments have been made :
After 2 years, the couple has made 2 * 12 = 24 payments.
Calculate the remaining balance using the Rule of 78 :
The sum of the digits from 1 to 30 (the number of payments) is given by the formula for the sum of an arithmetic series:
S = 2 n ( n + 1 ) = 2 30 ( 30 + 1 ) = 465
Find the sum of the digits for the remaining 6 payments (30 payments - 24 payments made): 1 + 2 + 3 + 4 + 5 + 6 = 21
The remaining interest according to the Rule of 78 is:
Remaining Interest = 465 21 × 570 = 465 21 × 570
Calculate the fraction:
Remaining Interest = 465 11970 ≈ 25.74
Calculate the total payoff amount :
The remaining principal balance is the remaining number of payments times the monthly installment:
Remaining principal = RM60 * 6 = RM360
Therefore, the payoff amount is the remaining principal balance plus the remaining interest:
Payoff amount = RM360 + RM25.74 = RM385.74
In conclusion, the couple should pay approximately RM385.74 to settle the balance immediately after 2 years using the Rule of 78.
