A simple question on bonds ?

Consider the example below (Please avoid too much jargon) :

Face value of a bond = $1000

(1) Issuing a bond at par –

coupon rate = market rate = 10% per year or 5% semi-annually.
present value or principal = 822.7
Interest = 177.3 (because an annuity of $50 is paid.)
TOTAL = 1000.

>>>what do i have to pay to purchase this bond ? 1000 or 822.7 ?
My textbook says that the company gets full use of the $1000, per bond.
>>>What does this mean ?


(2)Issuing bond at a discount –

market rate = 12 % , coupon = 10 %
present value or principal = 792.1
Interest = 173.25
TOTAL = 965.35

The textbook says that the company RECEIVES 963.35 per bond.

>>>Why not ask people to pay 1000 instead of 965.35 and offer them interest at market rate instead of these calculations ?

NOTE : This is taken form the book “Introduction to financial accounting” by horngren, sundem and eliott.
@JKRB – you said “and the discount of 36.35 makes up for the interest the buyers are losing for purchasing the 10% bonds when the market rate is 12%”.

Can you show mathematically, that the investors are losing 36.65 ? Then it would be easier to see that a lower selling price would make the interest higher.
My book presents the concept in a rather confusing way.
I was looking for some kind of mathematical proof which will show :

money lost by investor due to low coupon = discount offered.
Hence, no money lost by investor.

How to cash bearer check from Union bank of india?

I won 1800 rupees in sports in my school and i got bearer check.
Pay Self written on it and i have signed back of it but i never went to bank to cash etc.
So i am getting little nervous pls help me out about the process.

Should i fill the slip?? Anything else needed?