b$)$In order to encourage long term saving among Kenyan youth, an innovative investment product has been launched by one of the leading commercial banks in Kenya. The features of this investment product are as follows;

$8\%$ pa compounded annually in the first $7$ years.

$10\%$ pa compounded semi$-$annually after the $7$th year upto the $15$th year. $12\%$ pa compounded quarterly after the $15$th year.

Upon celebrating his $30$th birthday, Alex intend to invest a sum of money with this calibrated investment scheme in anticipation to raise Kshs $30,000,000$ at the attainment of $55$ years.

i$)$ Evaluate the percentage growth of the investment during the period under consideration.

ii$)$ Formulate the effective interest rate of the investment.

iii$)$ Discuss the implications of the assumptions made in the investment scheme.$(2$ Marks$)$