2. [Maximum mark: 6] On 1st January 2020, Laurie invests $P in an account that pays a nominal annual interest rate of 5.5%, compounded quarterly. The amount of money in Laurie's account at the end of each year follows a geometric sequence with common ratio, r. (a) Find the value of r, giving your answer to four significant figures. [3] Laurie makes no further deposits to or withdrawals from the account. (b) Find the year in which the amount of money in Laurie's account will become double the amount she invested. [3]