Independent solution

How to solve this Macaulay Duration from Price Sensitivity question

Setup

Setup

Relate the yield derivative of price to modified duration.

Dmod=−P′(i)P(i)D_{\mathrm{mod}}=-\frac{P'(i)}{P(i)}

Model

Model

Insert the price and derivative at the stated yield.

Dmod=−−4,750950=5D_{\mathrm{mod}}=-\frac{-4{,}750}{950}=5

Compute

Compute

Convert modified duration to Macaulay duration.

DMac=(1+i)Dmod=1.09(5)=5.45D_{\mathrm{Mac}}=(1+i)D_{\mathrm{mod}}=1.09(5)=5.45

Answer

Answer

The Macaulay duration is 5.45 years, choice E.

DMac=5.45(E)\boxed{D_{\mathrm{Mac}}=5.45\quad\text{(E)}}