The annually compounded discount rate is $9\mathrm{.}0\%.$ You are asked to calculate the present value of a $18-$year annuity with payments of

$$50,900$ per year.

a$.$ Calculate the PV if the annuity payments arrive at one$-$year intervals. The first payment arrives one year from now.

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ 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.$).$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

a$.$ Present value

b$.$ Present value