What is the market price (to the nearest dollar)of a 16% p.a.quarterly coupon bond with a face value of $100,five years to go until maturity when the current market yield is 12% p.a.?

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The market price of a bond can be calculated using the formula for the present value of its future cash flows, which include the periodic coupon payments and the face value repayment at maturity. For a bond with a 16% annual coupon rate, paid quarterly, the coupon payment per quarter is $4 (16% of $100, divided by 4). With a market yield of 12% per annum, the quarterly yield is 3% (12% divided by 4). The bond has 20 quarters left until maturity (5 years times 4 quarters per year).The present value of the coupon payments (an annuity) can be calculated using the formula: PV = C * [1 - (1 + r)^-n] / r, where C is the coupon payment per period, r is the market yield per period, and n is the total number of periods. Substituting the values, we get: PV(coupons) = $4 * [1 - (1 + 0.03)^-20] / 0.03 ≈ $61.35.The present value of the face value (a lump sum) can be calculated using the formula: PV = F / (1 + r)^n, where F is the face value. Substituting the values, we get: PV(face value) = $100 / (1 + 0.03)^20 ≈ $55.21.Adding the present values of the coupon payments and the face value gives the bond's market price: $61.35 + $55.21 ≈ $116.56. Since the options are rounded to the nearest dollar and there's no option exactly matching $116.56, the closest option is B) $114.

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