Question

#17 You purchased a 14-year, $1,000 bond with a 4.6% semi-annual coupon three years ago at a price of $1,015. Today you sold the bond at a price of $1,111. What was the yield to maturity when you sold the bond?

A. 3.84%

B. 3.38%

C. 4.45%

D. 5.33%

Answer 1

Face Value =	1000
semiannual Coupon Amount = 1000*4.6%*1/2 =	23
Number of Semiannual periods (n) at time of sale= 14-3 = 11 years*2=	22
sale price of bond =	1111
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(i) is that Semiannual rate at which bond price will be equal to current market price.
So Assume i=1.6%
bond price = 23*(1-(1/(1+1.6%)^22))/1.6% + 1000/(1+1.6%)^22
1128.956443
assume (i) =1.7%
bond price = 23*(1-(1/(1+1.7%)^22))/1.7% + 1000/(1+1.7%)^22
1109.361323
interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))
1.6% +((1.7%-1.6%)*(1128.956443-1111)/(1128.956443-1109.361323))
0.01691637321
annual yield to maturity =	0.03383274642
So annual yield to maturity is 0.0338 or 3.38%