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 product: For the first $70,000 you obtain 8% p.a. (per annum) for 10 years. For the other amount you obtain 2% p.a. for the first six years. Then you obtain 1% p.a. for the rest. (Interest payments are compounded.) Bank B offers you the following product: The interest in year 1 is 1%, in year 2 is 2%, in year 3 is 3%, in year 4 is 4%, then for years 5 to 10 you obtain 9% p.a. For both plans, interest payments are reinvested.
(a) You maximize the final amount. Which plan is better? How much more can you spend then, if you choose 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 you so that you get the same amount as from bank A?