Question

Question 3 x Your answer is incorrect. Try again. You have just purchased a municipal bond with a $10,000 par value for $9,500. You purchased it immediately after the previous owner received a semiannual interest payment. The bond rate is 6.6% per year payable semiannually. You plan to hold the bond for 4 years, selling the bond immediately after you receive the interest payment. If your desired nominal yield is 6% per year compounded semiannually, what will سل* be your minimum selling price for the bond? $1. Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is £5. Click here to access the TVM Factor Table Calculator

Answer 1

Current purchase price of the bond = V = 9,500

Selling price of bond = F =?

Semi-annual interest payment (I) = (Par value × bond rate) / m = (10,000 × 6.6%)/2 = 330

Yield to maturity (YTM) = 0.06

Number of remaining years (n) from the date of current purchase = 4

Number of semi-annual payments in a year (m) = 2

V = {I / (YTM/m)} [[{(1 + YTM/m)^(n×m)} – 1] / {(1 + YTM/m)^(n×m)}] + [F / {(1 + YTM/m)^(n×m)}]

9,500 = {330 / (0.06/2)} [[{(1 + 0.06/2)^(4 ×2)} – 1] / {(1 + 0.06/2)^(4 × 2)}] + [F / {(1 + 0.06/2)^(4 × 2)}]

Now, by solving as below,

9500 = 11,000 [(1.03^8) – 1] / 1.03^8] + [F / 1.03^8]

9500 = 11,000[(1.26677 – 1) / 1.26677] + [F / 1.26677]

9500 = 11,000(0.26677 / 1.26677) + [F / 1.26677]

9500 = 11,000 × 0.21059 + [F / 1.26677]

9500 = 2,316.49 + [F / 1.26677]

9500 – 2,316.49 = F / 1.26677

7,183.51 × 1.26677 = F

F = 9,099.85

   = 9,100 rounded to whole number

Answer: required price is $9,100.