You purchased 10 year bonds at an issue price of $990 whose face value is $1000. The annual coupon rate is 3%. What is the YTM? Five years later market rates of interest are 5%. What will be the price of the bonds? If you expect interest rates to hold at 5% or less, what should you do with the bonds?

What is the YTM?

Five years later market rates of interest are 5%. What will be the price of the bonds?

If you expect interest rates to hold at 5% or less, what should you do with the bonds?

Explanation:

YTM = {30 + [(1,000 - 990)/10]} / [(1,000 + 990)/2] = 31 / 995 = 0.03115 = 3.12%

5 years later:

5% = {30 + [(1,000 - MV)/5]} / [(1,000 + MV)/2]

0.05 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/5]

(0.05 x 500) + (0.05 x 0.5MV) = 30 + 200 - 0.2MV

25 + 0.025MV = 230 - 0.2MV

0.225MV = 205

MV = 205 / 0.225 = $911.11

in 6 years:

5% = {30 + [(1,000 - MV)/4]} / [(1,000 + MV)/2]

0.05 x [(1,000 + MV)/2] = 30 + [(1,000 - MV)/4]

(0.05 x 500) + (0.05 x 0.5MV) = 30 + 250 - 0.25MV

25 + 0.025MV = 280 - 0.25MV

0.275MV = 255

MV = 255 / 0.275 = $927.27

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