GAMA expects to retire $40$ years from $1$ow and currently contributes to AKIBA Pension Fund. GAMA wishes to increase his income during his retirement and he decides to invest Tshs $200,000$ in a murual fund for the purpose of adding up to his retirement income. GAMA found the following Funds operating in the market

$\backslash$table$[[$Charges$,\backslash$table$[[$Akiba Index Tracker$],[$Fund$]],\backslash$table$[[$Mafao Actively Managed$],[$Fund$]]],[$Initial Charges,$0,5\%$ of the value of investment$],[\backslash$table$[[$Annual$],[$Management$],[$charges$]],\backslash$table$[[0\mathrm{.}6\%$ of the value of the$],[$fund$]],1\mathrm{.}2\%$ of the value of the fund$],[\backslash$table$[[$Other cost including$],[$brokerage fees per year$]],\backslash$table$[[0\mathrm{.}2\%$ of the value of the$],[$fund$]],1\mathrm{.}4\%$ of the value of the fund$]]$

The Central Bank has provided that the long term the average real rate of rerurn on a balanced portfolio of shares is $6\%$ per year and such performance is expected to continue for the next $10$ years, on the assumption that the funds match the general market perfomtance.

Required:

$($i$)$ What is the annual total expense ratio $($including the brokerage fees$)$ in each Fund?

$($ii$)$ What do you expect the value of the Akiba index tracker tund to be after $10$ years?

$($iii$)$ What are the effects of the expenses on the expected average annual return of the Akiba tracker fund?

$($iv$)$ What do you expect the value of Mafao actively managed fund to be after $10$ years?

$($v$)$ What are the effects of the expenses on the average annual return of the Mafao actively managed fund?

$($vi$)$ What would be the effects of charges on the expected average annual returns of each fund if the investment horizon were $5$ years rather than $10$ years?