$19\mathrm{.}22.$ What is the Macaulay duration of an eight$-$year, $10\%,$ interest$-$only mortgage with

annual payments occurring at the ends of the years? What is the modified duration

of this same mortgage?

$19\mathrm{.}23.$ What are the Macaulay and modified durations of an eight$-$year, $10\%,$ interest$-$only,

monthly$-$payment mortgage?