10.1 Index Number

10.1 Index Number

Example 1
The price of the house Sulaiman bought in the year 1998 was RM 110000. In the year 2000, the price of the house went up to RM 130000. Calculate the price index of the house for the year 2000 based on the year 1998.

Solution:
$\begin{array}{l}{P}_0=RM110000\\ P_1=RM130000\\ I=\frac{P_1}{P_0}\times 100\\ I=\frac{130000}{110000}\times 100\\ I=118.18\end{array}$

Example 2
The price of a bottle of cooking oil in the year 1999 was RM15.00. Given that the price index for the year 2000 based on the year 1999 is 105, calculate the price of the cooking oil in the year 2000.

Solution:
$\begin{array}{l}{P}_0=RM15\\ P_1=x{\text{ (Price}}_{2000})\\ I=\frac{P_1}{P_0}\times 100\\ 105=\frac{x}{15}\times 100\\ 1575=100x\\ x=RM15.75\end{array}$

Example 3
Based on the year 1995, the index number of an oven for the years 1998 and 2001 are 110 and 130 respectively. Find the index number for the year 2001 based on the year 1998.

Solution:
$\begin{array}{l}\text{Given, }\frac{P_{1998}}{P_{1995}}\times 100=110\text{ and }\frac{P_{2001}}{P_{1995}}\times 100=130\\ \therefore \frac{P_{2001}}{P_{1998}}\times 100=\frac{P_{2001}}{P_{1995}}\times \frac{P_{1995}}{P_{1998}}\times 100\\ =\frac{130}{100}\times \frac{100}{110}\times 100\\ \text{=118}\text{.18}\end{array}$