What is the current price of a financial security that pays a fixed coupon of 10.2% per annum per $100 face value,compounding half-yearly and maturing in four years,when current yields in the market are 8.6% per annum?
A) $103.9575
B) $70.3185
C) $103.887
D) $132.8295

Question

Quizplus · Accepted Answer

The price of a bond can be calculated using the present value of its future cash flows, which include the periodic coupon payments and the face value at maturity. Given a fixed coupon rate of 10.2% per annum (or 5.1% per half-year), a face value of $100, a market yield of 8.6% per annum (or 4.3% per half-year), and a maturity of 4 years (or 8 half-years), the bond's price is calculated as follows:$$ \text{Price} = \frac{C}{r} \left(1 - \frac{1}{(1+r)^n}\right) + \frac{F}{(1+r)^n} $$Where:- $C$ is the half-yearly coupon payment (\$100 * 5.1% = \$5.1),- $r$ is the half-yearly market yield (4.3% or 0.043 as a decimal),- $n$ is the total number of half-year periods (4 years * 2 = 8),- $F$ is the face value of the bond (\$100).Plugging in the values:$$ \text{Price} = \frac{\$5.1}{0.043} \left(1 - \frac{1}{(1+0.043)^8}\right) + \frac{\$100}{(1+0.043)^8} $$$$ \text{Price} \approx \$103.9575 $$Therefore, the correct choice is A, indicating the bond is priced at approximately \$103.9575, reflecting its value above par due to its coupon rate being higher than the current market yield.

What Is the Current Price of a Financial Security That