Ten annual returns are listed in the following$$ table:$($Click on the following icon in order to copy its contents into a$$ spreadsheet.$)$

negative $19\mathrm{.}5\%$

$16\mathrm{.}2\%$

$18\mathrm{.}3\%$

negative $49\mathrm{.}3\%$

$43\mathrm{.}9\%$

$1\mathrm{.}2\%$

negative $16\mathrm{.}5\%$

$45\mathrm{.}8\%$

$44\mathrm{.}7\%$

negative $3\mathrm{.}1\%$

a$.$ What is the arithmetic average return over the$10-$year period?

b$.$ What is the geometric average return over the$10-$year period?

c$.$ If you invested$$ $$100$ at the$$ beginning, how much would you have at the$$ end?

Question content area bottom

Part $1$

a$.$ What is the arithmetic average return over the$10-$year period?

The arithmetic average return over the$10-$year period is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $2$

b$.$ What is the geometric average return over the$10-$year period?

To find the geometric average$$ return, use the following formulas.

First find the future value of investing$$ $$1$ today, using the following$$ formula:

FV equals $ $1$ times left parenthesis left parenthesis $1$ plus Upper R $1$ right parenthesis times left parenthesis $1$ plus Upper R $2$ right parenthesis times times times times times left parenthesis $1$ plus Upper R Subscript Upper T right parenthesis right parenthesis

Then use the following formula and solve for R$$:

FV equals $ $1$ times left parenthesis $1$ plus Upper R right parenthesis Superscript $10$

The geometric average$$ return, $$R$,$ over the$10-$year period is

$$

enter your response here$\%.($Round to four decimal$$ places.$)$

Part $3$

c$.$ If you invested$$ $$100$ at the$$ beginning, how much would you have at the$$ end?

If you invested$$ $$100$ at the$$ beginning, at the end you would have $$$

$$

enter your response here. $($Round to the nearest$$ cent.$)$