Question

Mary buys a 10 year bond with $10,000 face value, semiannual nominal bond rate 3%, and semiannual nominal yield rate 4%. She wants to reinvest the semiannual coupons (immediately after each coupon is received) into a fund so that her non time valued net profit at maturity (A.V. of coupons + face value at maturity − bond price) is $5,000. Find the interest rate (as a semiannual nominal rate) that the account must earn for this to occur.

Answer 1

Face Value F=10000

Coupon rate =3%

Semi annual coupon C=3%*10000/2=150

Semi annual Yield r=4%/2=2%

Number of Years =10

Number of coupon payment N=10*2=20

Price of Bond P=C*(1-(1+r)^-N)/r + F/(1+r)^N

P=150*(1-(1+2%)^-20)/2% + 10000/(1+2%)^20

P=$9182.43

Let i be semi annual reinvest rate

AV of Coupon after 10 years AV=C*((1+i)^N-1)/i

AV=150*((1+i)^20-1)/i

AV+F-P=5000

150*((1+i)^20-1)/i+10000-9182.43=5000

((1+i)^20-1)/i=27.88

i=3.36%

So Annual Nominal rate =2*i=6.72%