q$\mathrm{.}1$Find what an investment grows to after $10$ years @ $10\%$ if

$1)$A sum of $100$ is deposited at the end of year $0$

$2)$A sum of $100$ is deposited each year for $10$ years, starting from year $0$

q$\mathrm{.}2$You have been offered a choice of three retirement planning investments.

The first investment offers a $5\%$ return for the first $5$ years, a $10\%$ return for the next $5$ years and a $20\%$ return thereafter.

The second investment offers a $10\%$ return for the first $10$ years and $15\%$ thereafter.

The third investment offers a constant $12\%$ rate of return.

Which of these is best for you if each requires you to pay the same amount each year and you plan to retire in the following number of years?:

$($a$)15$ years $($b$)20$ years $($c$)30$ years