a$)$ Holly Foods Market, Inc. has an obligation to pay its supplier $$441,000$ on

December $31,2052,$ two years from today. Suppose that the manager of the firm wants to

prepare for this upcoming payment. If the firm can earn a risk$-$free rate of $5\%$ per year, what is

the amount of funds needed today, December $31,2050?$

$*$For full credit, you must show the steps$/$calculation toward your results. b$)$ Today is December $31,2060.$ You expect to receive two payments, $$30,000$ at the end of $2063$ and $$40,000$ at the end of $2064.$ Upon receiving each payment, you will invest

them at $5\%$ per year until the end of $2069.$ What will the value of your investment be at the

end of $2069?$ Provide your results in two decimal places $($e$.$g$.,600\mathrm{.}7378=600\mathrm{.}74).$

$*$For full credit, you must show the steps$/$calculation toward your results.