Respuesta :
The current value is $1,032.98.
What is the appropriate discount rate?
- The yield to maturity of a bond is the appropriate discount rate (YTM).
- The YTM represents the return an investor will receive if he or she holds the bond until maturity.
- The YTM and bond price are linked; if we know one, we can figure out the other.
To find the current value:
Let,
- C = bond semiannual coupon = 10% / 2 × 1,000 = $50
- r = semiannual interest rate (discount rate, YTM) = 9% / 2 = 4.5%
- n = number of semiannual periods = 4 × 2 = 8
The price of a bond can be calculated using a formula.
This is the formula:
[tex]\begin{aligned}&\text { Price }=C * \frac{1-(1+r)^{-n}}{r}+\frac{\text { Par }}{(1+r)^n} \\&\text { Price }=50 * \frac{1-(1+0.045)^{-8}}{0.045}+\frac{1,000}{(1+0.045)^8} \\&\text { Price }=\$ 1,032.98\end{aligned}[/tex]
Therefore, the current value is $1,032.98.
Know more about discount rates here:
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The correct question is given below:
What is the current value of a $1,000 bond with a 10% annual coupon rate (paid semi-annually) that matures in 4 years if the appropriate stated annual discount rate is 9%?
