A bond has a face value of $1,000 and coupon payments of $120 annually.This bond matures in three years and is selling in the market for $1,160.Market interest rate is 6 percent.What is this bond's duration?
A)3 years
B)5.71 years
C)1.96 years
D)2.71 years
E)None of the options is correct.

Question

Quizplus · Accepted Answer

The formula to calculate duration is:

Duration = [CF₁/(1+r) + 2CF₂/(1+r)² +...+ nCFₙ/(1+r)^n] / Bond price

Where CF₁, CF₂, CF₃ are the cash flows of the bond at year 1, year 2 and year 3 respectively, r is the market interest rate and n is the number of years until bond maturity.

Plugging in the values, we get:

Duration = [120/(1+0.06) + 120/(1+0.06)² + 120/(1+0.06)³ + 1000/(1+0.06)³] / 1160
Duration = 2.71 years

Therefore, the bond's duration is 2.71 years. Option D is the correct choice.

A Bond Has a Face Value of $1,000 and Coupon