Bonds

Ref
"ABC Corporation issued bonds worth $1,000,000 face value on January 1, 1990. Semi-annual interest payments are due on July 1 and January 1. The bonds were scheduled to mature on January 1, 2000."

Case I: Issuing Bonds Above Par Value-premium
Market rate of interest = 3%
Coupon rate = 4%.
Since the market rate of interest is below the coupon rate, bonds will be issued at premium or above par value.
company borrowed $1,085,884 at the prevailing market rate of interest which is three percent. In the first period, the interest expense for six months is $16,288 (= 1,085,884 x .03 x 0.5). However, the company paid $20,000 (=1,000,000 x .04 x 0.5) to bondholders. Since the amount paid to bondholders is greater than the interest expense, the excess payment is considered a repayment of principal and is subtracted from the outstanding loan. As a result, the outstanding loan decreases by $3,712 (=20,000-16,288). The second period begins with the loan outstanding at the end of first period. Again, since the company is paying more amount than the interest, the excess payment goes towards principal and reduces the outstanding loan amount.

Case II: Issuing Bonds Below Par Value - Discount
Market rate of interest = 4%
Coupon rate = 3%.
Company borrowed $918,206 at 4% interest rate. In the first period, the interest expense for six months is $18,364 (= 918,206 x .04 x 0.5). However, the company paid only $15,000 to bondholders. Since the company has not paid the full interest amount, the shortfall ($3,364 = 18,364 - 15,000) is added to the outstanding loan amount. As a result, the outstanding loan increases by $3,364 and is now $921,570 (= 918,206 + 18,364) at the end of the first period. We start out the second period with the loan outstanding at the end of the first period. In the second period, the interest expense for six months is $18,431. Since the company is not paying the entire interest amount, the unpaid interest ($3,431 = 18,431 - 15,000) is again added to the outstanding loan amount.