Mary purchased a 10-year par value bond with semiannual coupons at a nominal annual rate of 4% convertible semiannually at a price of 1021.50. The bond can be called at par value 1100 on any coupon date starting at the end of year 5. What is the minimum yield that Mary could receive, expressed as a nominal annual rate of interest convertible semiannually?

0.05628 = 5.628%

The minimum yield that Mary could receive is 5.628%

Explanation:

Using the YTM (yield to maturity) formula

YTM = C + (f - p) /n ÷ (f+p) /2

C = coupon rate ; 4% of 1,100(par value) = 4/100 × 1,100 = 44

f = face value ( par value) = 1,100

P = market price = 1021.50

n = number of years = (10 - 5)= 5years : since the bond could be called at the end of 5 years.

YTM = 44 + (1,100 - 1,021.50)/5 ÷ (1,100+1,021.50)/2

YTM = 44 + ( 78.5)/5 ÷ 2121.5/2

YTM = 59.7/1,060.75

YTM = 0.05628

= 5.628% as the minimum yield Mary could receive.

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