Question $2.$A$.2(40\backslash \%)$

Jenny currently makes $\backslash (30,000\backslash )$ a year as a librarian. She is considering a career change: For a current expenditure of $\backslash (9,000\backslash ),$ she can become a florist. If she makes that career change, her earnings will rise to $\backslash (35,000\backslash )$ per year. Jenny has four years left to work before retirement $($it is assumed that she gets paid once at the end of each year$).$

A$.$ If the interest rate is $\backslash (10\backslash \%\backslash ),$ calculate the net present value of Jenny's investment in flower arrangement lessons

B$.$ Assuming that being a florist offers the same job satisfaction as being a librarian, should Jenny change career?

C$.$ Would Jenny choose differently if at the end of her career as a librarian she receives a lump$-$sum bonus of $\backslash (12,000\backslash )?$

Question $2.$B$.3(40\backslash \%)$

Suppose that Sally's utility function $\backslash ($ U $\backslash )$ is given by $\backslash ($ U$=$w$^\{0\mathrm{.}5\}\backslash ),$ where $\backslash ($ w $\backslash )$ is wealth. Sally has a wealth of $20$ and is thinking of buying a pleasure boat which would cost $10$ of her wealth. The probability that she buys the boat is $\backslash (20\backslash \%\backslash ).$

$($a$)$ Calculate Sally's expected value of wealth

$($b$)$ Calculate Sally's level of utility at the expected value of wealth.

$($c$)$ Calculate Sally's expected utility

$($d$)$ Is Sally risk$-$averse?

$($e$)$ What is Sally's certainty equivalent?

$($f$)$ What is Sally's risk premium?

All sub$-$questions carry equal marks