The annually compounded discount rate is $5\mathrm{.}5\%.$ You are asked to calculate the present value of a $11-$year annuity with payments of $$50,200$ per year. Calculate the PV if the annuity payments arrive at one$-$year intervals. The first payment arrives one year from now. Calculate the PV if the first payment arrives in six months. Following payments arrive at one$-$year intervals $($i$.$e$.,$ at $18$ months, $30$ months, etc.$).$