Question

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

Answer 1

Answer:

Option E (143) is the appropriate solution.

Explanation:

According to the question,

The modified duration will be:

= $\frac{Macaulay \ duration}{(1+yield)}$

= $8\times 1.064$

= $8.512$

The percentage change in price will be:

= $-0.6\times 8 \ percent$

= $-4.8$ (%)

Now,

The EMOD will be:

= $112955\times (1-4.8 \ percent)$

= $107533.2$ ($)

Or,

The EMAC will be:

= $112955\times (\frac{1.064}{1.07} )^{8.512}$

= $107675.7$ ($)

Hence,

⇒ $EMOD-EMAC=107533.2-107675.7$

                                  $=-142.5$

⇒ $EMAC-EMOD=143$