Your grandpa would like to share some of his fortune with you. He offers to give you money under one of the following scenarios$($you get to$$ choose$)$:

$1.7550$ a year at the end of each of the next years

$2.50,050($lump sum$)$ now

$3.100,050($lump sum$)$ years from now

Calculate the present value of each scenario using $6\%$ interest rate. Which scenario yields the highest present$$ value? Would your preference change if you used a $12\%$ interest$$ rate?