Question

A $10 000, 8.2% bond with semi-annual coupons is purchased 3 years before maturity. Calculate the discount or premium if the bond is sold to yield 6% compounded semi-annually.

Answer 1

Given coupon rate is 8.2% with semi annual coupon payments for a bond with face value of 10000. So, Coupon payment is 820/2= 410. Yield is 6% compounded semi annually. So, for every six months, yield will be 3%.

Price of the bond is calculated using the formula: P= C/(1+r)+C/(1+r)^2+....(C+P)/(1+r)^n; where C is the coupon payment per period, P is the face value of the bond, r is the yieldnto maturity and n is the number of years to maturity.

So, Price of the bond= 410/1.03+410/1.03^2+410/1.03^3+410/1.03^4+410/1.03^5+410/1.03^6+10000/1.03^6

= $10595.89

So, Premium on the bond= $595.89