$As$ winner $of$ a breakfast cereal competition, you can choose one $of$ the following prizes:

$a.If$ the interest rate $is12\%,$ find the $PV$ for each $of$ the prizes. $(Do$ not round intermediate calculations. Round your answer $to2$

decimal places.$)$

$b.$ Which $is$ the most valuable prize?

$$100,000$ now.

$$180,000at$ the end $of$ five years.

$$11,400$ a year forever.

$$19,000$ for each $of10$ years.

$$6,500$ next year and increasing thereafter $by5\%$ a year forever.