SPM Mathematics Trial 2021 (Selangor), Paper 2 (Question 17)

Question 17 (15 marks):
Hanis just got promoted as a manager in a private company in Johor Bahru with monthly salary of RM12 000 . She wants to buy a new car model Proton X 701.8 L Premium with the price of RM124 000 with a bank loan.

(a) She makes a comparison and found out that the two banks that offer best loan packages are as below:

Loan aspects	Bank Sejahtera	Bank Tenang
Sum of loan	100%	90%
Interest rate	3.1%	2.5%
Payment period	9 years	7 years
Total repayment	RM 158 596

Table 4.1

Table 4.1, total loan repayment of Bank Tenang is not stated. 
(i) Calculate the total loan repayment with Bank Tenang. 
(ii) Calculate the monthly installment for both banks.
[6 marks]


Solution:
(a)(i)

$\begin{array}{l}\underset{\_}{\text{Bank Tenang:}}\\ \text{Sum of loan}=\frac{90}{100}\times 124500=\text{RM }111600\\ \\ \text{Interest rate incurred for 7 years}\\ =\text{RM }111600\times \frac{2.5}{100}\times 7\\ =\text{RM }19530\\ \\ \therefore \text{ Total repayment}\\ =\text{RM }111600+\text{RM }19530\\ =\text{RM }131130\end{array}$


(a)(ii)

$\begin{array}{l}\underset{\_}{\text{Bank Sejahtera:}}\\ \text{Payment period}=\text{9}\times 12=108\text{ months}\\ \text{Monthly installment}=\frac{\text{RM }158596}{108}=\text{RM }1468.48\\ \\ \underset{\_}{\text{Bank Tenang:}}\\ \text{Payment period}=7\times 12=84\text{ months}\\ \text{Monthly installment}=\frac{\text{RM }131130}{84}=\text{RM }1561.07\end{array}$

(b):
After almost a full year since Hanis bought a new car, she needs to renew her road tax. The engine capacity of her car is 1799 cc.
Table 4.2 shows the road tax rates for private car in Peninsular Malaysia.

Engine capacity	Road tax rate
	Base rate	Progressive rate
1 401 cc – 1 600 cc	RM90.00
1 601 cc – 1 800 cc	RM200.00	+ RM0.40 each cc exceeding 1 600 cc
1 801 cc – 2 000 cc	RM280.00	+ RM0.50 each cc exceeding 1 800 cc
2 001 cc – 2 500 cc	RM380.00	+ RM1.00 each cc exceeding 2 000 cc

Table 4.2

(i) Who collects road tax on behalf of Malaysian government?

(ii) What is the basic rate of road tax, in RM, for Hanis’s car?

(iii) Hence, calculate the amount of road tax that Hanis have to pay. 
[4 marks]


Solution:
(b)(i)
Road Transport department or Jabatan Pengangkutan Jalan or JPJ collects road tax on behalf of Malaysian government.

(b)(ii)
The engine capacity of Hanis’s car is 1799 cc, thus the basic rate of road tax for her car is RM200.00.

(b)(iii)
Amount of road tax that Hanis have to pay
= base rate of road tax + progressive rate for each cc exceeding 1 600 cc
= RM200 + (1799 – 1600) × RM0.40
= RM279.60