Question

Calculate the price of a 9.8 percent coupon bond with 17 years left to maturity and a market interest rate of 5.6 percent. (Assume interest payments are semiannual.) (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Bond price

$

    

Is this a discount or premium bond?

Discount bond Premium bond

Answer 1

Formula for Bond Price is:

Bond Price = C x [1-{1/ (1+r) ⁿ}/r] +M/(1+r)ⁿ

M = Face Value = $ 1,000 [Assumed]

C= Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

= ($ 1,000 x 9.8 %)/2 = = ($ 1,000 x 0.098)/2 = $ 98/2 = $ 49

r = Rate of interest = 5.6 % or 0.056/2 = 0.028 semiannually

n = No of periods to maturity = 17 years x 2 = 34 periods

Bond Price = $ 49 x [1-{1/ (1+0.028)³⁴}/0.028] + $ 1,000/ (1+0.028)³⁴

                 = $ 49 x [1-{1/ (1.028)³⁴}/0.028] + $ 1,000/ (1.028)³⁴

               = $ 49 x [1-{1/ 2.557207081}/0.028] + $ 1,000/2.557207081

                 = $ 49 x [(1-0.391051631)/ 0.028] + $ 391.051631

                = $ 49 x [0.608948369/0.028] + $ 391.051631

                = $ 49 x 21.74815604 + $ 391.051631

              = $ 1,065.659646 + $ 391.051631

               = $ 1,456.711277 or $ 1,456.71

It is a premium bond as it is trading above its par value.