A couple borrows $$200,000$ for a mortgage that requires fixed monthly payments over $30$ consecutive years. The first monthly payment is due in one month. If the interest rate on the mortgage is $6\%,$ which of the following comes closest to the monthly payment?

A$.$

$ $1,101$

B$.$

$ $1,074$

C$.$

$ $1,199$

D$.$

$ $1,211$

E$.$

$ $843$Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the $$Set for Life$$ Prize that makes $20$ consecutive annual payments of $$50,000$ starting immediately. There is one exception: the eleventh payment $($to be received at the end of year $10)$ is not $$50,000$ but only $$20,000($that is$,$ this one payment is $$30,000$ LESS than the other $19).$ Which of the following comes closest to the present value of the prize if interest rates are $6\%?$

A$.$

$ $543,496$

B$.$

$ $635,849$

C$.$

$ $591,154$

D$.$

$ $577,906$

E$.$

$ $970,000$Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the $$Set for Life$$ Prize that makes $20$ consecutive annual payments of $$50,000$ starting immediately. There is one exception: the eleventh payment $($to be received at the end of year $10)$ is not $$50,000$ but only $$20,000($that is$,$ this one payment is $$30,000$ LESS than the other $19).$ Which of the following comes closest to the present value of the prize if interest rates are $6\%?$

A$.$

$ $543,496$

B$.$

$ $635,849$

C$.$

$ $591,154$

D$.$

$ $577,906$

E$.$

$ $970,000$