a$.$ Assuming that the expectations hypothesis is valid, compute the expected price of the four$-$year zero coupon bond below at the start of $($i$)$ the first year; $($ii$)$ the second year; $($iii$)$ the third year; $($iv$)$ the fourth year. $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

$\backslash$table$[[\backslash$table$[[$Beginning$],[$of Year$]],$Price of Bond,Expected Price,$],[1,$$$,963\mathrm{.}40,],[2,$$$,908\mathrm{.}47,],[3,$$$,857\mathrm{.}62,],[4,$$$,783\mathrm{.}16,]]$

b$.$ What is the rate of return of the zero bond in years $1,2,3,$ and $4?$ Conclude that the expected return equals the forward rate for each year. $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

$\backslash$table$[[\backslash$table$[[$Beginning$],[$of Year$]],\backslash$table$[[$Expected Rate of$],[$Return$]]],[1,,\%$