As a financial planner, suppose you observe a client with the lifetime utility .

With an interest rate of 20% and a lifetime wealth of $2000, answer the questions below.

1. What equilibrium current and future consumption level would you recommend to this client? (Show all calculations)
2. What is the client's lifetime utility from current and future consumption?
3. suppose there is an increase in lifetime wealth from $2000 to $2500. show how this will affect the equilibrium future, current consumption bundles, and lifetime utility. (show all steps and calculations).
4. Suppose the interest rate drops from 20% to 15% and lifetime wealth remains $2000, show how the client will smooth current and future consumption. (show all steps and calculations).
5. How do the impacts of changes in lifetime wealth and interest rates on current and future consumption differ?