A $5000 bond pays interest at j₂ = 4% and is redeemable at par in 5 years.The desired yield is j₂ = 5%.What price should you pay for this bond if the probability of any payment being defaulted is 1%,given that all previous payments were paid? A)$4792.45 B)$4733.39 C)$4561.24 D)$4362.69

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the bond using the given information:
PV = (5000 x 0.04) x ((1 - (1 + 0.04)^-5)/0.04) + 5000/(1+0.04)^5
PV = $4,514.07
Next, we need to adjust the price to account for the default risk. We can do this using the following formula:
Adjusted price = PV x (1 - probability of default)
Adjusted price = $4,514.07 x (1 - 0.01)
Adjusted price = $4,469.93
Finally, we need to calculate the purchase price that would give us a yield of 5%:
Purchase price = PV / (1 + yield)^(number of years to maturity)
Purchase price = $4,469.93 / (1 + 0.05)^5
Purchase price = $3,733.39

Therefore, the best choice is B.

A $5000 Bond Pays Interest at J2 = 4% and Is

A $5000 Bond Pays Interest at J₂ = 4% and Is