Final answer:
The fixed base index is calculated by dividing the price of the security for each month by the base month price and multiplying by 100. Between August and January, the security price increased by approximately 4.52%. Between September and December, the security price increased by approximately 15.38%.
Step-by-step explanation:
To calculate the fixed base index for the security's price with August as the base month (index = 100), we divide the price of the security in each subsequent month by the price in August, and then multiply by 100. Applying this formula, we can create the following index values for each month:
August (Base): Price = 155, Index = 155 / 155 * 100 = 100
September: Price = 143, Index = 143 / 155 * 100 ≈ 92.26
October: Price = 120, Index = 120 / 155 * 100 ≈ 77.42
November: Price = 139, Index = 139 / 155 * 100 ≈ 89.68
December: Price = 165, Index = 165 / 155 * 100 ≈ 106.45
January: Price = 162, Index = 162 / 155 * 100 ≈ 104.52
To calculate the percentage change in security price:
August to January: The index moved from 100 to 104.52, which is a change of (104.52 - 100) / 100 * 100% ≈ 4.52% increase.
September to December: The index moved from 92.26 to 106.45, which is a change of (106.45 - 92.26) / 92.26 * 100% ≈ 15.38% increase.