You are considering buying $$100,000$ face value of a $10\%$ coupon $($semiannual payments$)$ treasury bond whose last coupon was $29$ days ago $($there are $181$ days in the current coupon period$).$ The price quote is $98-25.$ How much will you pay if you buy this bond?

None of the choices are correct

$$98,250$

$$100,000$

$$98,781$

$$99,582$