Q$5($b$)$ Today the prices of a $1$ risk$-$free bond to be paid in one, two and three years are, respectively, $0\mathrm{.}95,0\mathrm{.}90$ and $0\mathrm{.}85.$

$($i$)$ What are the implied interest rates?

$($ii$)$ What is the present value of a risk$-$free bond that pays $100$ per year over the next three years?