An engineer starting his career wishes to build up a lump sum fund at the time of his retirement, 30 years from today. For this reason, he decides to save every year a fixed annual amount in his deposit account which today (time zero) has a balance of €10,000. Deposits start today and will be completed one year before retirement (in time 29). 

Consider the interest rate on bank deposits to be variable. Answer the following questions and comment on the results, where appropriate.

(a) If the annual deposit amount is 2,000 and the annual interest rate on deposits is 3% for the first 15 years and 7% for the remaining 15 years, what amount will be accumulated in the account by the time of his retirement (time 30)?

(b) Would it change anything compared to the result of question (a) if the annual interest rate on deposits is 7% for the first 15 years and 3% for the remaining 15 years. Also compare the results with those of question (a).

(c) If the deposits are made every two years (0, 2, 4, ..., 28) with an amount twice that of the previous cases, i.e. A΄= €4,000, and the annual interest rate of the deposits is 3% in the first 15 years and 7% the remaining 15 years, what amount will be accumulated in the account by the time of his retirement (time 30)?