A $20 000, 3.6% bond with semi-annual coupons is purchased 5 years before maturity. Calculate the discount or premium if the bond is sold to yield 3% compounded semi-annually.

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The bond's price is determined by the present value of its future cash flows, which include the semi-annual coupon payments and the face value repayment at maturity. The coupon payment is $20,000 * 3.6% / 2 = $360 every six months. Since the bond is sold to yield 3% compounded semi-annually, the discount rate per period is 1.5% (3% / 2). There are 10 periods remaining (5 years * 2). The present value of the coupon payments is an annuity: PV = C * [1 - (1 + r)^-n] / r = $360 * [1 - (1 + 0.015)^-10] / 0.015 = $3,118.50. The present value of the face value is: PV = F / (1 + r)^n = $20,000 / (1 + 0.015)^10 = $17,434.83. The total price of the bond is the sum of these two present values: $3,118.50 + $17,434.83 = $20,553.33. Since the bond is sold for $20,553.33 and its face value is $20,000, it is sold at a $553.33 premium.