What is the duration of a zero coupon bond with ﬁve years to maturity that is currently priced at $980 and has an interest rate of 8%?

Question

Quizplus · Accepted Answer

A zero coupon bond does not pay interest, but is sold at a discount from its face value and matures at face value. In this case, the bond is priced at $980 and has a face value of $1000 ($1000-$980 = $20 discount). The interest rate is 8%, so we can use the formula to find the duration:

Duration = (ln(FV/Price))/(ln(1+YTM/2))

where FV is the face value, Price is the current price, YTM is the yield to maturity, and ln is the natural logarithm.

Plugging in the numbers:

Duration = (ln(1000/980))/(ln(1+0.08/2)) = 4.98 years

Therefore, the duration of the bond is approximately 5 years. Answer D is correct.

What Is the Duration of a Zero Coupon Bond with ﬁVe