Question

You just purchased a $1,000 par bond with a 6% semi-annual coupon and 15 years to maturity at par. You are hoping that interest rates fall and that you will be able to sell the bond in seven years at a price $1,200. What will the yield to maturity of the bond have to be to get the price you want in seven years?

A. 3.15% B. 4.19% C. 4.55% D. 1.57%

Answer 1

*2

Years to Maturity at time of sale = 15-7= 8

Semiannual periods (n)= 8*2= 16

Face value =1000

Semiannual Coupon =1000*6%/2 = 30

Required Market value of bond at year 7 =1200

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

Here coupon is Semiannual Coupon, so yield (i) is Semiannual yield.

Yield to maturity is that rate where bond price will be equal to current market price.  
  
So Assume i=1.5%  
bond price = 30*(1-(1/(1+1.5%)^16))/1.5% + 1000/(1+1.5%)^16

=1211.968961

Assume i is 1.6%

Bond price = 30*(1-(1/(1+1.6%)^16))/1.6% + 1000/(1+1.6%)^16

=1196.251745

interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))
1.5% +((1.6% -1.5%)*(1211.968961-1200)/(1211.968961-1196.251745))
=0.01576151915

Annualized yield to Maturity =0.01576151915*2

=0.0315230383 or 3.15%

So yield to Maturity should be 3.15% at that time