A $100 bond with semi-annual coupons,redeemable at 105 in 8 years,can be purchased at a discount of $18.19 to yield j₂ = 12%.What is the bond coupon rate,j₂?

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The bond coupon rate can be found by setting up the equation for the bond's price based on its cash flows and solving for the coupon rate. The bond's price is given as $100 - $18.19 = $81.81. It pays semi-annual coupons, is redeemable at $105 in 8 years (which equals 16 semi-annual periods), and is meant to yield a semi-annual rate of 6% (12% annual rate divided by 2). Let C be the semi-annual coupon payment. The price of the bond can be represented by the present value of its cash flows:$$81.81 = \frac{C}{0.06} \left(1 - \frac{1}{(1+0.06)^{16}}\right) + \frac{105}{(1+0.06)^{16}}$$Solving this equation for C gives the semi-annual coupon payment. To find the annual coupon rate, we multiply the semi-annual coupon payment by 2 and then divide by the bond's face value ($100) and convert to a percentage. The correct calculation leads to a coupon rate of 16.2%, indicating that option D is correct.

A $100 Bond with Semi-Annual Coupons,redeemable at 105 in 8