Question

Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Answer 1

Answer:

$828.36

Explanation:

As for the information provided,

The value = $1,000

Life = 20 years, since interest is semi annual, effective period = 20 $\times$ $\frac{12}{6}$ = 40 periods.

Semi annual interest = $40

Annual interest = 10%, effective interest rate = 5%

Future Value Interest rate = $40 $\times (\frac{1}{(1+0.05)^1} +\frac{1}{(1+0.05)^2} +\frac{1}{(1+0.05)^3} +\frac{1}{(1+0.05)^4} +\frac{1}{(1+0.05)^5} +\frac{1}{(1+0.05)^6} +\frac{1}{(1+0.05)^7} +.................. + \frac{1}{(1+0.05)^4^0} )$

= $40 $\times$ 17.159 = $686.36

Future Value of Principal = $1,000 $\times \frac{1}{(1 + 0.05)^4^0}$

= $1,000 $\times$ 0.142 = $142

Thus, current price of bond = $686.36 + $142 = $828.36