$7\mathrm{.}2\mathrm{.}5$ A liability of $1$ is due at time $10.$ An attempt is made to fully

immunize this liability at $i_0=\mathrm{.}10$ using two zero coupon bonds

of amounts $A_{t_1}$ and $A_{t_2}$ due at times $t_1$ and $t_2,$ respectively. In

each of the following cases, solve for the two missing quantities

out of $A_{t_1},A_{t_2},t_1,t_2,$ given the other two.

$($a$)t_1=5,t_2=15$

$($b$)($i$)t_1=5,A_{t_1}=\mathrm{.}40$

$($ii$)t_1=5,A_{t_1}=\mathrm{.}70($no solution for $t_{2}10)$