An investor deposited $15,000 into a special variable interest savings account 15 years ago. With no further deposits or withdrawals, the account value has grown to $80,000 now. It was known that during the initial years, interest was paid semi-annually at a nominal rate of 10% per annum convertible semi-annually. That is, the account balance was updated every half a year during this initial period. Once the account balance exceeded $20,000, the interest rate changed, and interest was paid quarterly for the next nine years. After that, the interest rate changed again to 9.45% per annum convertible monthly, and payment frequency changed to monthly. In short, this investment experienced three distinct accumulation phases in the last 15 years whereby the interest rates and payment frequencies were different under each phase. a) Calculate the length of the first and last accumulation phases in units of half-years and months respectively. [6 marks] b) Calculate the annual nominal interest rate convertible quarterly that was applicable during the second accumulation phase. [4 marks]