You buy a bond with the following features: 6 years to maturity, face value of $

Question

You buy a bond with the following features: 6 years to maturity, face value of $1000, coupon rate of 4% (annual coupons) and yield to maturity of 2.1%. Just after you purchase the bond, the yield to maturity rises to 4.5%. What is the capital gain or loss on your bond? If the answer is a capital gain just enter the number. For example 581.65 If the answer is a capital loss enter a negative number. For example -841.47 Do not include the $ sign, just enter the number in dollars, rounded to the nearest cent (2 decimals). Hint: capital gain / loss = value of the bond now - initial value of the bond.

Explanation / Answer

We know the formulae YTM = (C + (F - P) / n) / ((F + P) / 2) YTM = Yield to Maturity C = Coupon or Interest Payment = 4 % of 1000 = $ 40 F = Face Value = $ 1000 P = Price = x n = Years to Maturity = 6 years 2.1 % = ( 40 +( 1000-x) /6)/((1000+x)/2) 2.1% = (1240-x)/6/(1000+x) /2 Bond price = 1106.08 $ if ytm = 4.5 % 4.5% = (1240-x)/6/(1000+x) /2 Bond price = 974.22 $ Therefore capital loss = -131.86 $ =974.22-1106.08

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