A $13-$ year bond with face and redemption amount $12,600$ pays semiannual coupons and was purchased for $P.$ The coupon rate is greater than the yield rate. The principal adjustment portion of the ${10}^{th}$ coupon was $17\mathrm{.}12$ and the principal adjustment portion of the ${25}^{th}$ coupon was $24\mathrm{.}08.$ Calculate $P.$

$($A$)12,111$

$($B$)12,948$

$($C$)13,089$

$($D$)13,142$

$($E$)13,244$