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

a$.$ $$100,000$ now.

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

c$.$ $$11,400$ a year forever.

d$.$ $$19,000$ for each of $10$ years.

e$.$ $$6,500$ next year and increasing thereafter by $5\%$ a year forever.

If the interest rate is $12\%,$ which is the most valuable prize?