Question

# #17 You purchased a 14-year, \$1,000 bond with a 4.6% semi-annual coupon three years ago at...

#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%

 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%

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