You are setting up a fund to support $1$ annual art grant $($$$2500$ yearly$)$ and $1$ biennial music grant $($$$5000$ every $2$ years$).$ Assume the fund earns $12\%$ per year,

$1.$ Calculate the amount you need to put in today to set up the fund?

$2.$ How sensitive is the initial trust sum to changes in the rate of return?