Question

You purchased a zero coupon bond one year ago for $121.53. The bond has a par value of $1,000 and the market interest rate is now 8 percent. If the bond had 27 years to maturity when you originally purchased it, what was your total return for the past year? Assume semiannual compounding.

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =26x2

Bond Price =∑ [(0*1000/200)/(1 + 8/200)^k]     +   1000/(1 + 8/200)^26x2

k=1

Bond Price = 130.1

Using Calculator: press buttons "2ND"+"FV" then assign

PMT = Par value * coupon %/coupons per year=1000*0/(2*100)

I/Y =8/2

N =26*2

FV =1000

CPT PV

Using Excel

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

=PV(8/(2*100),2*26,-0*1000/(2*100),-1000,)

rate of return/HPR = ((Selling price+Coupon amount)/Purchase price-1)

=((130.1+0)/121.53-1)

=7.05%