A 7% Commonwealth Government bond has three years to maturity.Given that the bond pays interest semi-annually (i.e.twice a year)and an interest payment has just been made,what is the present value of the bond if the market interest rate is 9% and the face value of the bond is $100 000?

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payments: 
$100,000 x 7% x 0.5 = $3,500 
Since the bond has just made an interest payment, there will be 5 more semi-annual interest payments left.

Using the formula for present value of a bond: 
PV = [C/(1+i)^1] + [C/(1+i)^2] + ... + [C+Face Value/(1+i)^n]

where C is the coupon payment, i is the market interest rate, and n is the number of periods until maturity, we can plug in the values:

PV = [$3,500/(1+0.045)^1] + [$3,500/(1+0.045)^2] + ... + [$3,500+ $100,000/(1+0.045)^6] 
PV = $3,295.45 + $3,106.80 + $2,928.02 + $2,757.59 + $2,594.98 + $70,159.29 
PV = $94,842.13

Therefore, the present value of the bond is $94,842.13 which is closest to option A) $94,842.13.

A 7% Commonwealth Government Bond Has Three Years to Maturity