When are the bonds issued at a premium and bonds issued at a discount?

The bonds are issued whenever the issuing body wants to issue them. They are discounted, sold at a premium or at par depending on how the issuing body prices them and how the market values them.

If the company is in trouble and has to accept less than par (face value of the bond) then it sells the bond for a discount. If the bonds are in demand and the seller can command a price higher than par, it sells for a premium.

Widgetcorp issues a $10,000 bond. If the bond sells for less than $10,000 it has sold at a discount. If it sells for $10,000 then it sells for par and if it is over $10,000 then it sells at a premium. The coupon, or interest rate doesn't matter.

Cost accounting is the accounting associated with the cost of producing your product. Financial accounting is the most general, it mainly focuses on accounting outside the company such as for taxes and auditing. Managerial accounting is more internal and is used mostly for making decisions about which direction to take a business.

You're talking about investment bonds, not insurance bonds. Wrong category.