Today is t=0t=0. You observe the following prices for options on stock A:

Type of option	Maturity (years)	Strike price	Price of option
Call	0.5	105	2
Call	1	105	3
Put	1	105	5
Put	1.5	105	7

All the above options are European. Stock A does not pay dividends. The risk-free rate is 5% per annum. In addition, you also observe the following trajectory for the price of stock A:

Time (years)	Price of stock A
t=0.5	120
t=1	110
t=1.5	100

You need the initial price of stock A at t=0 in order to compute your taxes. Unfortunately, you lost this value. Use put-call parity to back out the initial price of stock A. What is your answer for the initial price of stock A?