Question

Compute the Macaulay duration for a 9-year zero-coupon bond having a yield to maturity of 13%....

Compute the Macaulay duration for a 9-year zero-coupon bond having a yield to maturity of 13%.

a.

7.96

b.

9.26

c.

7.70

d.

9.00

e.

8.92

please explain in steps

Homework Answers

Answer #1

Macaulay duration is the weighted average time to maturity of a bond.

The formula for macaulay's duration is

Where, PV is the present value of the bond at a given yield to maturity.

C1, C2, C3, ... CT the cash flows from the bond at time period 1, 2, 3, .... , T respectively.

Now, since the given bond is a Zero coupon bond, therefore is only one cash flow, i.e at the end of the period.

Thus, C1, C2, C3, are all 0

Thus, duration = 0 + 0 + 0 + ...............+ 9 * PV (CT) / PV

Since the present value of the future cash flow is same as the present value of the bond, therefore

Duration = 9 years.

Explained differently, duration of a zero coupon bond is always the years to maturity since the whole amount is to be received at the end of the maturity.

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