Question

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 3.5% per year compounded semiannually, what will be your minimum selling price for the bond?

Answer 1

ANSWER:

Semi annual coupon payment = par value * bond rate / 2 = 10,000 * 6.6% / 2 = 330

IN 4 years there will be 8 payments (4 * 2)

Semi annual discount rate = nominal yield / 2 = 3.5% / 2 = 1.75%

Par value = Semi annual coupon payment(p/a,i,n) + selling price(p/f,i,n)

9,500 = 330(p/a,1.75%,8) + f(p/f,1.75%,8)

9,500 = 330 * 7.41 + f * 0.8704

9,500 = 2,443.67 + 0.8704 f

0.8704 f = 9,500 - 2,443.67

0.8704 f = 7,056.33

p = 7,056.33 / 0.8704

p = 8,106.997

so the minimum selling price of bond will be $8,106.997 or $8,107