The $1-$year spot rate is $8\%$ p$.$a$.$ effective. The term structure of $1-$year effective

forward rates is as follows: at time $t=1$ the rate is $7\%,$ at time $t=2$ the rate

is $6\%,$ at time $t=3$ the rate is $5\%.$

$($a$)$ Determine the term structure of spot rates.

$($b$)$ A fixed income security pays $10$ annual coupons and it is redeemed after

$4$ years for $100.$ Compute its price at time $t=0.$