The following is a list of prices for zero$-$coupon bonds of various maturities.

Maturity $($years$)$ Price of Bond

$1$ $ $960\mathrm{.}90$

$2904\mathrm{.}97$

$3846\mathrm{.}12$

$4780\mathrm{.}76$

Required:

Calculate the yield to maturity for a bond with a maturity of $($i$)$ one year; $($ii$)$ two years; $($iii$)$ three years; $($iv$)$ four years. Assume annual coupon payments.

Calculate the forward rate for $($i$)$ the second year; $($ii$)$ the third year; $($iii$)$ the fourth year. Assume annual coupon payments.