please show work and formulas used for calculations. thanks

36. Growing perpetuities and annuities 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