Question

Your brother has just invested in a discount bond that offers an annual coupon rate of 9%, with interest paid annually. The face value of the bond is $1,000 and the difference between its yield to maturity and coupon rate is 4%. The bond matures in 8 years. What is the bond’s price?

Answer 1

1) If the  yield to maturity is more than coupon rate by 4 percentage points:

$P=\frac{C*(1-1/1.09^8)}{1-1/1.09}+\frac{1000*1.13}{1.09^8}$

P-price of bond

C-coupon$=1000*0.09=90$

$P=\frac{90*(1-1/1.09^8)}{1-1/1.09}+\frac{1000*1.13}{1.09^8}=1,110.07$

2) If the  yield to maturity is less than coupon rate by 4 percentage points:

$P=\frac{90*(1-1/1.09^8)}{1-1/1.09}+\frac{1000*1.05}{1.09^8}=1,069.93$