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?

Respuesta :

Answer:

$828.36

Explanation:

As for the information provided,

The value = $1,000

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

Semi annual interest = $40

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

Future Value Interest rate = $40 [tex]\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} )[/tex]

= $40 [tex]\times[/tex] 17.159 = $686.36

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

= $1,000 [tex]\times[/tex] 0.142 = $142

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

The maximum price you should be willing to pay for the bond should be $828

Calculation of maximum price:

Since The time period = 20 × 2 = 40

Future value = $1,000

PMT = $40

NPER = 10% ÷2

The below formula should be used

=-PV(RATE,NPER,PMT,PV,FV,TYPE).

After applying the above formula, the maximum price should be $828.

Learn more about price here: https://brainly.com/question/24349694

ACCESS MORE
EDU ACCESS
Universidad de Mexico