Question

4) A school has been keeping track of the school fee in its music program over the past few years from 2018 to 2020. The school fee each year is as follows: $1500, $1600, $1700.

a) Calculate the index numbers using 2018 as the base year
b) If the inflation rates in 2019 and 2020 increased by 10% and 5%, respectively, what was the real school fee in 2018 adjusted for the base year 2019? What was the real enrollment rate in 2020 adjusted for the base year 2019?

Answer 1

a) To calculate the index numbers using 2018 as the base year, we divide each year's school fee by the 2018 school fee and multiply by 100:

- Index number for 2018 = (1500/1500) x 100 = 100
- Index number for 2019 = (1600/1500) x 100 = 106.7
- Index number for 2020 = (1700/1500) x 100 = 113.3

Therefore, the index numbers using 2018 as the base year are 100, 106.7, and 113.3 for 2018, 2019, and 2020, respectively.

b) To find the real school fee in 2018 adjusted for the base year 2019, we need to use the index numbers for 2018 and 2019. The formula is:

Real value in base year = (Nominal value / Index number) x 100

Using this formula, we can find the real school fee in 2018 adjusted for the base year 2019:

Real school fee in 2018 = (1500/106.7) x 100 = $1407.50

So, the real school fee in 2018 adjusted for the base year 2019 is $1407.50.

To find the real enrollment rate in 2020 adjusted for the base year 2019, we need to use the index numbers for 2019 and 2020. Since we don't have the enrollment rate data, let's assume that the enrollment rate remained constant at 80% in all three years. Then, the nominal enrollment rate and the real enrollment rate adjusted for the base year 2019 would be:

- Nominal enrollment rate in 2020 = 80%
- Real enrollment rate in 2020 = (80/113.3) x 100 = 70.6%

So, the real enrollment rate in 2020 adjusted for the base year 2019 is 70.6%.