a$)$ Briefly explain on the three $(3)$ main reasons as to why institutional investors prefer investing in a passively managed fund. $[6$ Marks$]$

b$)$ A Tanzanian investor is considering a $5-$year investment of TZS $350$ million in a foreign mutual fund that uses an index tracker fund. The index tracker fund has no initial charge, but charges an annual management fee of $1\mathrm{.}3\%$ of the value of the fund and average annual share dealing costs of $0\mathrm{.}7\%.$

Based on the latest information given in the Financial Times newspaper, the long term average real rate of return on a balanced portfolio of shares is $5\mathrm{.}4\%$ p$.$a$.,$ and the performance is expected to continue for the next $5$ years. On the assumption that the funds match the general market performance:

i$)$ Briefly explain on how an index tracker fund works. $[2$ Marks$]$

ii$)$ What is the annual total expense ratio? $[4$ Marks$]$

iii$)$ What is the expected value of the index tracker fund after $5$ years? $[6$ Marks$]$

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