The Macaulay duration for the $16-$year, $7\mathrm{.}5\%$ coupon bond in Problem $1$ is approximately $10$:

Comment on the relation between duration, horizon date, and bond immunization.

Year t Cash Flow PVt at $6\%$ PV$/$P $($PV$/$P$)$ t

$17570\mathrm{.}75470\mathrm{.}06140\mathrm{.}0614$

$27566\mathrm{.}74970\mathrm{.}05800\mathrm{.}1159$

$37562\mathrm{.}97140\mathrm{.}05470\mathrm{.}1640$

$47559\mathrm{.}40700\mathrm{.}05160\mathrm{.}2063$

$57556\mathrm{.}04440\mathrm{.}04870\mathrm{.}2433$

$67552\mathrm{.}87200\mathrm{.}04590\mathrm{.}2755$

$77549\mathrm{.}87930\mathrm{.}04330\mathrm{.}3032$

$87547\mathrm{.}05590\mathrm{.}04090\mathrm{.}3269$

$97544\mathrm{.}39240\mathrm{.}03850\mathrm{.}3469$

$107541\mathrm{.}87960\mathrm{.}03640\mathrm{.}3637$

$117539\mathrm{.}50910\mathrm{.}03430\mathrm{.}3774$

$127537\mathrm{.}27270\mathrm{.}03240\mathrm{.}3884$

$137535\mathrm{.}16290\mathrm{.}03050\mathrm{.}3969$

$147533\mathrm{.}17260\mathrm{.}02880\mathrm{.}4033$

$157531\mathrm{.}29490\mathrm{.}02720\mathrm{.}4076$

$161075423\mathrm{.}16980\mathrm{.}36755\mathrm{.}8795$

P $1151\mathrm{.}58843$ Dur