Your annual salary is $$100,000.$ You are offered two options for a severance package. Option $1$ pays you $6$ months$$ salary now. Option $2$ pays you $$4,000$ per year for $20$ years $($the payments are at the end of each year$).$

$1.$ If your required rate of return is $6\%,$ which should you chose.

$2.$ Plot the values of Option$1$ and Option$2$ as a function of interest rates where rates vary from $0$ to $15\%.$

$3.$ Which investment is more sensitive to changes in interest rates? Why does this make sense?