In the late $1980$s you could earn interest rates of $12\%,$ compounded annually, on a guaranteed investment certificate $($GIC$).$ At that time, with a GIC you were locked into the investment for a fixed period $($commonly $5$ years but you could negotiate longer or shorter periods$).$

$($a$)$ How long would it take to double your investment?

$($b$)$ Today you are unlikely to earn more than $5\%,$ compounded annually. How long would it take to

double your money now?