A husband and wife are planning for retirement and they believe that a comparison over a fiveyear period would be appropriate. They are given the following information about one mutual fund that they are considering. Assume that all remaining assets under management are withdrawn by the family at the end of $5$ years.

$\backslash$table$[[$Year$,\backslash$table$[[$Beginning Assets$],[$Under Management$]],$Net Return $(\%)],[1,30\mathrm{.}000\mathrm{.}000,16\%],[2,35\mathrm{.}000\mathrm{.}000,12\%],[3,25\mathrm{.}000\mathrm{.}000,-17\%],[4,15\mathrm{.}000\mathrm{.}000,-3\%],[5,20\mathrm{.}000\mathrm{.}000,6\%]]$

a$.$ Compute the arithmetic and geometric mean annual return for the fund.

b$.$ What is the money$-$weighted annual return for the fund? You can calculate the annual cash flow $($either additional investment or withdrawal by the couple$)$ at year $t$ as the difference between the beginning assets under management at year $t$ and ending assets under management at year $t-1.$