Consider a mutual fund with $$200$ million in assets at the start of the year and with $10$ million shares outstanding. The fund invests in a portfolio of stocks that provides dividend income at the end of the year of $$2$ million. The stocks included in the fund's portfolio increase in price by $8\%,$ but no securities are sold, and there are no capital gains distributions. The fund charges $12$b$-1$ fees of $1\%,$ which are deducted from portfolio assets at year$-$end.

$$

Required:

a$.$ What is the net asset value at the start and end of the year? $($Enter your answers in dollars rounded to $3$ decimal places.$)$

b$.$What is the rate of return for an investor in the fund?$($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

$$

TimePriceAction$0$$ $90$Buy $3$ shares$1100$Sell $1$ share$2100$Sell $1$ share$3100$Sell $1$ share

$$

Required:

a$.$ Calculate the time$-$weighted geometric average return on this portfolio. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$.$ Calculate the time$-$weighted arithmetic average return on this portfolio. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

$$

c$.$ Calculate the dollar$-$weighted average return on this portfolio. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$