$1.$ A mutual fund offers $"$A$"$ shares, which have a $5\%$ upfront load and an expense ratio of $0\mathrm{.}76\%.$ The fund also offers $"$B$"$ shares, which have a $3\%$ back$-$end load and an expense ratio of $0\mathrm{.}87\%.$ Which shares make more sense for an investor looking over an $18-$year horizon?$2.3.$ A mutual fund reported year$-$end total assets of $$1,508$ million and an expense ratio of $0\mathrm{.}90\%.$ What total fees is the fund charging each year?$4.$ A $$1$ million fund is charging a back$-$end load of $1\%,12$b$-1$ fees of $1\%,$ and an expense ratio of $1\mathrm{.}9\%.$ Prior to deducting expenses, what must the fund value be at the end of the year for investors to break even?Questions $6-12$ trace a sequence of transactions involving a single mutual fund$\mathrm{.}6.$ On January $1,$ a mutual fund has the following assets and prices at $4$:$00$ PM$.$StockShares ownedPrice$11,000$$$1\mathrm{.}9725,000$$$48\mathrm{.}2631,000$$$26\mathrm{.}44410,000$$$67\mathrm{.}4953,000$$$2\mathrm{.}591.$ Calculate the net asset value $($NAV$)$ for the fund$\mathrm{.}2.$ Assume that $8,000$ shares are outstanding for the fund$\mathrm{.}3.7.$ An investor sends the fund a check for $$50,000.$ If there is no front$-$end load, calculate the new number of shares and price per share. Assume the manager purchases $1,800$ shares of stock $3,$ and the rest is heldas cash$\mathrm{.}4.5.8.$ On January $2,$ the prices at $4$:$00$ PM are as follows:StockShares ownedPrice$1,000$$$2\mathrm{.}0325,000$$$51\mathrm{.}3732,800$$$29\mathrm{.}08410,000$$$67\mathrm{.}1953,000$$$4\mathrm{.}42$Cashn.a$.$$$2,408\mathrm{.}00$Calculate the net asset value $($NAV$)$ for the fund$\mathrm{.}1.$ Assume the new investor then sells the $420$ shares.What is his profit? What is the annualized return? The fund sells $800$ shares of stock $4$ to raise the needed funds. Assume $250$ trading days per year$\mathrm{.}2.$ To discourage short$-$term investing in its fund, the fund now charges a $5\%$ upfront load and a $2\%$ back$-$end load. The same investor decides to put $$50,000$ back into the fund. Calculate the new number of shares out$-$standing. Assume the fund manager buys back as many round$-$lot shares of stock $4$ with the cash$\mathrm{.}11.$ On January $3,$ the prices at $4$:$00$ pMare as follows:StockShares ownedPrice$11,000$$$1\mathrm{.}9225,000$$$51\mathrm{.}1832,800$$$29\mathrm{.}0849,900$$$67\mathrm{.}1953,000$$$4\mathrm{.}51$Cashn.a$.$$$5,353\mathrm{.}401.$ Calculate the new NAV$\mathrm{.}2.12.$ Unhappy with the results, the new investor then sells the $389\mathrm{.}09$ shares. What is his profit? What is the new fund value?