What is the Macaulay duration of a 76 percent coupon bond wi

What is the Macaulay duration of a 7.6 percent coupon bond with seven years to maturity and a current price of $1,032.20? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Solution

Step 1: Calculate Market Rate of Interest

The market rate of interest can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Coupon Payment, PV = Bond Price and FV = Face Value.

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Here, Nper = 7, PMT = 1,000*7.6% = $76, PV = 1,032.20 and FV = 1,000

Using these values in the above formula, we get,

Market Rate of Interest = Rate(7,76,-1032.20,1000) = 7%

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Step 2: Calculate Macaulay Duration:

The Macaulay Duration is calculated with the use of following table:

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Step 3: Calculate Modified Duration:

The Modified Duration is calculated as follows:

Modified Duration = Macaulay Duration/(1+(Market Rate of Interest/Compounding Frequency))

Here, Macaulay Duration = 5.704, Market Rate of Interest = 7% and Compounding Frequency = 1 (as the bond is Annual)

Modified Duration = 5.704/(1+(7%/1)) = 5.330 Years