Question

Find the face value of the 20-year zero-coupon bond at 4.4%, compounded semiannually, with a price of $8,375.

Answer 1

Given:

Time,

t = 20 years

Rate,

r = 4.4%

Price

= $8,375

Now,

The yield will be:

= $\frac{4.4}{2}$

= $1.1$ (%)

Time will be:

= $20\times 2$

= $40 \ periods$

As we know the formula,

⇒ $Price \ of \ bond = \frac{Face \ value}{(1+\frac{r}{2} )^{n\times 2}}$

By substituting the values, we get

                   $8375=\frac{Face \ value}{(1+\frac{0.044}{2} )^{20\times 2}}$

                   $8375=\frac{Face \ value}{(1.022)^{40}}$

                   $8375=\frac{Face \ value}{2.3880083}$

The face value will be:

        $Face \ value = 2.3880083\times 8375$

                           $=20,000$ ($)

Learn more about face value here:

brainly.com/question/14862802