Liabilities of $1$ each are due at the ends of periods $1$ and $2.$ There are three securities available to produce asset income to cover these liabilities, as follows:

$($i$)$ A bond due at the end of period $1$ with coupon at rate $1\%$ per period, valued at a periodic yield of $14\%$;

$($ii$)$ A thond due at the end of period $2$ with coupon rate $2\%$ per period, valued at a periodic yield of $15\%$;

$($iii$)$ A bond due at the end of period $2$ with coupon rate $20\%$ per period, valued at a periodic yield of $14\mathrm{.}95\%$