Compute the Macaulay duration for a 9year zerocoupon 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 
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.
C_{1,} C_{2}_{,} C_{3, ...} C_{T} 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, C_{1,} C_{2}_{,} C_{3,} are all 0
Thus, duration = 0 + 0 + 0 + ...............+ 9 * PV (C_{T}) / 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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