Suppose you have $100,000 today that you want to save for 10 years. Compare the following two savings plans.
Bank A offers you the following alternative:
For the first $50,000 you obtain 6% p.a. (per annum) for 10 years. For the other amount you obtain 4% p.a. for the first four years. Then you obtain 3% p.a.
Bank B offers you 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 you obtain 1% p.a.
For both plans, interest payments are reinvested.
(a) You maximize the amount at t=10. Which plan is better? How much more can you spend at t=10, if you choose the better one? [4p]
(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 you so that you get the same amount as from bank A?