A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is $1,000. It matures in four years. Its yield to maturity is currently 6%.
-The duration of this bond is _______ years.

Question

Quizplus · Accepted Answer

To calculate the duration of the bond, use the following formula:
Duration = [∑(t*Ct)/(1+y)^t]/BV
Where:
t = time period until cash flow is received
Ct = cash flow at time period t
y = yield to maturity
BV = bond value
Using the information given:
C1 = $90 (9% of $1,000)
C2 = $90 (9% of $1,000)
C3 = $90 (9% of $1,000)
C4 = $1,090 (coupon + par value)
y = 6%
BV = $1,000
Plugging into formula:
Duration = [1*(90/1.06) + 2*(90/1.06^2) + 3*(90/1.06^3) + 4*(1,090/1.06^4)]/$1,000
Duration = 3.56 years. Therefore, the best choice is C.

A Bond Pays Annual Interest