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A bond has a modified duration of 8 and a price of 112,955 calculated using an annual effective interest rate of 6.4%. EMAC is the estimated price of this bond at an interest rate of 7.0% using the first-order Macaulay approximation EMOD is the estimated price of this bond at an interest rate of 7.0% using the first-order modified approximation Calculate EC EMOD A. 91 B. 102 C. 116 D. 127 E. 143

Sagot :

Cricetus

Answer:

Option E (143) is the appropriate solution.

Explanation:

According to the question,

The modified duration will be:

= [tex]\frac{Macaulay \ duration}{(1+yield)}[/tex]

= [tex]8\times 1.064[/tex]

= [tex]8.512[/tex]

The percentage change in price will be:

= [tex]-0.6\times 8 \ percent[/tex]

= [tex]-4.8[/tex] (%)

Now,

The EMOD will be:

= [tex]112955\times (1-4.8 \ percent)[/tex]

= [tex]107533.2[/tex] ($)

Or,

The EMAC will be:

= [tex]112955\times (\frac{1.064}{1.07} )^{8.512}[/tex]

= [tex]107675.7[/tex] ($)

Hence,

⇒ [tex]EMOD-EMAC=107533.2-107675.7[/tex]

                                  [tex]=-142.5[/tex]

⇒ [tex]EMAC-EMOD=143[/tex]

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