Problem
Ingrid is considering of buying an insurance today. Insurance A will pay $150,000 starting next year, and for the first five years the annual payments would increase by 2% each year. Thereafter she will receive a fixed payment of $300,000 each year till forever. The interest rate is 8% annually.
I. What is the value of this insurance package today?
II. Ingrid is also considering another insurance option (Insurance B) in which it will pay her $50,000 starting the end of this year, and each year the payments will increase by 6% till forever. Should Ingrid choose this option instead?
III. How much does the annual payment need to grow each year in option B so that Ingrid will be indifferent from choosing between Insurance A and Insurance B?