Suppose an agent has $100,000 today that he wants to save for 10 years. Compare the following two savings plans. Bank A offers the following alternative: For the first $50,000 the agent obtains 8% p.a. (per annum) for 10 years. For the other amount he obtains 4% p.a. for the first four years. Then he obtains 1% p.a. Bank B offers the following alternative: The interest in year 1 is 2%, in year 2 is 4%, in year 3 is 8%, in year 4 is 20%, then for years 5 to 10 the agent obtains 3% p.a. For both plans, interest payments are reinvested. (a) The agent maximizes the amount at t=10. Which plan is better? How much more can he spend at t=10, if he chooses the better one? (b) Suppose bank B wants to match the offer of bank A. Interest rates for years 2 to 10 are as above. What interest rate for the first year must bank B offer the agent so that he gets the same amount as from bank A?