Consider a $120-$day maturity bond having a quoted price of $91$ and Face Value $$100.95$ days have passed, and the quoted price increased to $93\mathrm{.}5.$ Calculate the price of the bond.

a$)$ $$69\mathrm{.}19$

b$)$ $$99\mathrm{.}55$

c$)$ $$97\mathrm{.}12$