A car costing $ $56598$ is purchased with a $25\%$ down payment and further payments of X at the beginning of every month for $10$ years. The annual nominal interest rate is $5\mathrm{.}6\%$ convertible semi$-$annually. Calculate X$.$

a$.$

$$478\mathrm{.}45$

b$.$

$$459\mathrm{.}31$

c$.$

$$473\mathrm{.}09$

d$.$

$$440\mathrm{.}94$

e$.$

$$261\mathrm{.}09$