You have just received a $1$ million inheritance. You have the following

four investment opportunities available:

i$.$ Investment in one$-$year government bonds yielding $5\%.$

ii$.$ A loan to your cousin, who wants to open a restaurant. Your cousin

had arranged a one$-$year bank loan for $900,000$ at $10\%,$ but asks you

for a $1$ million loan at $9\%.$

iii. Investment in the stock market, which has an expected rate of return

of $12\%.$

iv$.$ Investment in local real estate, which you judge is about as risky as

the stock market. The opportunity you are considering will cost you $1$

million and is forecasted to be worth $1\mathrm{.}1$ million after one year.

$4$ of $6$

Which of these investments have positive NPVs$?$ Which would you take?