he expected annual effective rate of return from an insurance company's investments is $6\%$ and the standard deviation of annual returns is $8\%.$ The annual effective returns are independent and $($l $+$ i$\_$t$)$ is lognormally distributed, where i$\_$t is the return in the t th year. $($a$)$ Calculate the expected value of an investment of pound$1$ million after ten years. $($b$)$ Calculate the probability that the accumulation of the investment will be less than $90\%$ of the expected value.