Question

5 years to maturity. 9 percent coupon. $1,000 face value, Market price (current) $1,126. annuals coupon payment.

what is duration of these bonds?

SHOW WORK

A- 3.77 YEARS

B- 4.23 YEARS

C- 5 YEARS

D- 9 YEARS

Answer 1

Bond Par Value = $ 1000, Annual Coupon Rate = 9 % per annum payable annually, Bond Tenure = 5 years, Market Price = $ 1126

Annual Coupon Payment = 0.09 x 1000 = $ 90

Let the yield to maturity be R

1126 = 90 x (1/R) x [1-{1/(1+R)^(5)}] + 1000/(1+R)^(5)

Using EXCEL's Goal Seek Function we get:

R = 6.008% per annum

As is observable the bond's duration is 4.28 years or approximately equal to 4.23 years. Hence, the correct option is (B).