On April 1, 20X4, Hill Corp. issued 200 of its $1,000 face value bonds at 101 plus accrued interest. The bonds were dated November 1, 20X3, and bear interest at an annual rate of 9% payable semiannually on November 1 and May 1. What amount did Hill receive from the bond issuance?

	$194,500
	$200,000
	$202,000
	$209,500

This Answer is Correct (Answer: D, $209,500)

The total proceeds on the bond issue equal the total bond price plus accrued interest. The latter amount is the cash interest between the bond issuance date (April 1, 20X4), and the most recent interest payment date before the bond issuance date (November 1, 20X3), a period of 5 months. The most recent interest payment date in this case is the bond date.

Total bond price: 200($1,000)(1.01)	$202,000
Plus accrued interest (5/12)($200,000)(.09)	7,500
Equals bond proceeds	$209,500

Question:

Can please explain in an easy way why $209,500 is the answer because I'm still not understanding why it is the answer regardless of the explanation above. Also why did they multiply by 1.01 for "Total bond price" in the above entry and why is the total proceeds on the bond issue equal the total bond price plus accrued interest? Please explain as easy as possible.