A $1000-$par value $30-$year bond has an annual coupon rate of $7\%$ paid semiannually. After an initial $10-$year period of call protection, the bond is callable immediately following the payment of any of the $20$th through the $59$th coupons.

i$)$ If the bond is called before payment of the $40$th coupon, the redemption value is $1250.$

ii$)$ If the bond is called immediately after the payment of any of the $40$th through the $59$th coupons, the redemption value is $1125.$

iii$)$ If the bond is not called, it will be redeemed at par.

To ensure that the bond will provide at least an annual nominal yield rate of $5\%$ convertible semiannually, it must be assumed that the bond will be called or redeemed immediately after the payment of the $n$th coupon.

Calculate $n.$

$($A$)20$

$($B$)39$

$($C$)40$

$($D$)59$

$($E$)60$