What is the current price of an existing Treasury bond that pays a fixed coupon of 6.4% per annum per $100 face value,compounding half-yearly,and maturing in four years? Current market yields are 6.8% per annum.
A) $22.0888
B) $44.1775
C) $76.5307
D) $98.6195

Question

Quizplus · Accepted Answer

To find the current price of the Treasury bond, we use the formula for the present value of a bond, which accounts for the present value of the bond's future coupon payments plus the present value of the bond's face value at maturity. Given that the bond pays a 6.4% annual coupon rate (compounded semi-annually, so 3.2% every six months) on a $100 face value and the market yield is 6.8% per annum (or 3.4% every six months), and the bond matures in 4 years (or 8 six-month periods), we can calculate the price as follows:$$ \text{Price} = \frac{C}{r} \left(1 - \frac{1}{(1+r)^n}\right) + \frac{F}{(1+r)^n} $$Where:- $C$ is the semi-annual coupon payment (\$100 * 3.2% = \$3.2),- $r$ is the semi-annual market yield (3.4% or 0.034 as a decimal),- $n$ is the total number of coupon payments (4 years * 2 = 8),- $F$ is the face value of the bond (\$100).$$ \text{Price} = \frac{\$3.2}{0.034} \left(1 - \frac{1}{(1+0.034)^8}\right) + \frac{\$100}{(1+0.034)^8} $$$$ \text{Price} = \$98.6195 $$Therefore, the current price of the Treasury bond is approximately \$98.6195.

What Is the Current Price of an Existing Treasury Bond