1) For how long must an investment be left at 5.5% p.a compounded yearly for the initial amount to double?

1(1.055)^n = 2

use logs

n log 1.055 = log 2
n = log2/log1.055
= appr 12.9 years

In the "olden days" we used something called the rule of 72
rate x time = 72
so here time = 72/5.5 = 13.09 , not bad