Problem $1$ Mutual Funds Suppose in the beginning of $2023$ and you invested in a mutual fund, GrowthPlus, which had a total of $25,000$ shares in the market and its investment portfolio has the following composition: $300$ shares of Stock W at $$25$ per share; $1,000$ shares of Stock X at $$60$ per share; $500$ shares of Stock Y at $$40$ per share; $800$ bonds of Bond Z at $$1,000$ each and $$40,000$ in cash. The fund also has liabilities totaling $$20,000.$ You held the investment until the end of $2024$ and following changes took place during the two$-$year investment horizon: End of Year $1$: Stock W appreciated by $4\%,$ Stock X appreciated by $5\%,$ Stock Y depreciated by $10\%,$ and Bond Z paid an annual interest of $$60$ per bond. GrowthPlus paid an annual dividend of $$5$ at the end of $2023$ to its shareholders. No changes take place to the cash and liabilities. End of Year $2$: Stocks W$,$ X and Y$$s values remain the same, but Bond Z paid an annual interest of $$60$ per bond. Also, the fund repaid its entire liabilities and held an additional cash of $$30,000.$ GrowthPlus paid an annual dividend of $$3.$ If the total number of shares remain unchanged during the period, calculate: a$.$ The initial NAV, and the NAVs at the end of each year of the GrowthPlus Fund. $(1+1$ mark$)$ b$.$ Your holding period yield for the investment in GrowthPlus. $(0\mathrm{.}5$ marks$)$ c$.$ Your annualized yield from the investment. $(0\mathrm{.}5$ marks$)$ Problem $2$ a$.$ Mutual fund X has sold $50,000$ shares to investors to raise funds and holds the following investment portfolio: $1,000$ shares of Stock A at a price of $$50$ per share; $500$ shares of Stock B at a price of $$30$ per share; $200$ bonds of Bond C at a price of $$100$ each. Additionally, the fund has $$10,000$ in liabilities. Calculate the Net Asset Value $($NAV$)$ of the mutual fund. $(1$ mark$)$ b$.$ For the same mutual fund with investments and quantities as in $($a$),$ let's say the fund's investments appreciated by $10\%$ in value in a year, but it also acquired $$20,000$ in additional liabilities during that period. Calculate the new Net Asset Value $($NAV$)$ of the mutual fund after these changes. $(1$ mark$)$