You have $$10000$ to invest. If you invest it at $11\mathrm{.}2\%$ p$.$a$.$ for six months, compounding annually then continue to invest the principal amount together with any interest for a further $12$ months at $12\mathrm{.}7\%$ p$.$a$.,$ compounding annually, what will be the value of your investment at the end of the $18-$month period?

$$11884\mathrm{.}37$

$$12532\mathrm{.}24$

$$11830\mathrm{.}00$

$$12241\mathrm{.}36$