Question

Assuming semi-annual compounding, what is the price of a zero coupon bond that matures in 3 years if the market interest rate is 5.5 percent? Assume par value is $1000.

Using semi-annual compounding, what is the price of a 5 percent coupon bond with 10 years left to maturity and a market interest rate of 7.2 percent? Assume that interest payments are paid semi-annually and that par value is $1000.

Using semi-annual compounding, what is the yield to maturity on a 4.65 percent coupon bond with 18 years left to maturity that is offered for sale at $1,025.95? Assume par value is $1000.

Answer 1

1.Semi annual payments shows the frequency of 2 periods in a year

number of periods=3*2=6

Price of a bond (P)= Par value/((1+(r%/2))^6)

P= $1000/(1+(5.5%)/2)^6

=$1000/(1.0275)^6

=$1000/(1.1767)

=$849.78

2.this bond coupons are paid semi annually, hence coupon payments are=(5%/2) *$1000=2.5%*1000=$25

Maturity=10 years

But the payment frequency is 2 in a year, hence the number of periods are 20(10 years*2)

This can be calculated using PV formual in excel

=PV(rate,nper, pmt,fv, type)

rate=7.2%, but input only for half a year which comes to 3.6%

=PV((7.2%/2),20,25,1000,0)

$845.07

3. Coupon rate= 4.65%

Yearly coupon payment=(4.65%*$1000)=$46.5

Semi annual payment=$46.5/2=$23.25

number of periods=18 years*2=36 periods

This can be calculated with RATE function in excel

=RATE(nper, pmt,pv,fv,type, guess)

=RATE(36,23.25,-1025.95,1000,0,0)

=2.22%

semi annual yield to maturity =2.22%

annual yield to maturity=2.22%*2=4.44%