Question

A $1,000 bond with a coupon rate of 6.6% paid semiannually has two years to maturity and a yield to maturity of 6.4%. If interest rates fall and the yield to maturity decreases buy 0.08%, what will happen to the price of the bond? A) rise by $20.97 B) fall by $17.97 C) rise by $14.98 D) fall by $14.98

Answer 1

Solution:

First we need to calculate the current price of bond(when YTM is 6.40%)

Price of bond=Present value of expected coupon+Present value of maturity amount

Coupon per period=($1000*6.6%)/2=$33

No. of period=2*2=4

YTM per period=6.4%/2=3.2%

Price of bond=$33*PVAF(3.2%,4)+$1000*PVIF(3.2%,4)

=$33*3.69939+$1000*0.88162

=$1003.70

Now,price of bond when YTM is 6.32%

YTM per period=6.32/2=3.16%

Price of bond=$33*PVAF(3.16%,4)+$1000*PVIF(3.16%,4)

=$33*3.70292+$1000*0.882988

=$1005.18

Thus price of bond is increase by $1.48 ($1005.18-$1003.70).Thus correct answer is Option C