Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non$-$number you should ever enter $($if appropriate$)$ is either a period as in $12\mathrm{.}34$ or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text $($e$.$g$.,$ do not type $$The answer is$),$ or punctuation $($except the period or minus sign if appropriate$).$ For example, if asked to round to the nearest $2$ decimal places, $$1,234\mathrm{.}567$ should be entered as $1234\mathrm{.}57,$ not as $$1,234\mathrm{.}57$ with the dollar sign, not as $-1234\mathrm{.}56$ which is rounded incorrectly, and if the answer were actually negative, then use a minus sign instead of entering $(1234\mathrm{.}57)$ using parentheses. If asked for the nearest integer, enter $1235($note the rounding$)$ and nothing else. If a rate of return of $12\mathrm{.}365\%$ is to be expressed in decimal format rounded to four decimal places, then the only as$-$requested answer is $0\mathrm{.}1237,$ not $0\mathrm{.}12365,$ not $12\mathrm{.}37,$ not $12\mathrm{.}365,$ not $12\mathrm{.}3650,$ or any other answer$).$ Please read again how your answer is to be expressed before entering it and enter it as requested.

You are considering buying a $1-$year maturity asset that has a $70\%$ chance of paying you $$180$ in one year and a $30\%$ chance of paying you $$151.$ If you are willing to pay at most $$143,$ what is your required rate of return? Express rounded to the nearest $4$ decimal places $($e$.$g$.,0\mathrm{.}1234).$ See the above for how to express answers$--$answer in decimal format $(12\mathrm{.}34\%$ should be entered as $0\mathrm{.}1234).$