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

Option E (143) is the appropriate solution.

Step-by-step explanation:

According to the question,

The modified duration will be:

=
`(Macaulay \ duration)/((1+yield))`

=
`8* 1.064`

=
`8.512`

The percentage change in price will be:

=
`-0.6* 8 \ percent`

=
`-4.8` (%)

Now,

The EMOD will be:

=
`112955* (1-4.8 \ percent)`

=
`107533.2` ($)

Or,

The EMAC will be:

=
`112955* ((1.064)/(1.07) )^(8.512)`

=
`107675.7` ($)

Hence,

⇒
`EMOD-EMAC=107533.2-107675.7`

`=-142.5`

⇒
`EMAC-EMOD=143`