A manufacturing firm purchased a heavy duty drilling machine. They were given two payment options:

Option $1$: Make a payment of $$40,500$ immediately to settle the invoice for the machine.

Option $2$: Make a payment of $$23,000$ immediately and the balance of $$23,550$ in $3$ months to settle the invoice.

If money is worth $4\mathrm{.}12\%$ compounded quarterly, answer the following:

a$.$ What is the total present value of Option $2?$

Round to the nearest cent

b$.$ Which option is economically better for the manufacturing firm?

Option $1$

Option $2$