Problem 1 (10 marks). Assume the annual fixed term deposit rate is 3.4% in a New Zealand bank. Mary has $10,000 and plans to deposit into the bank for two years. She also wants the bank to reinvest her interests. The bank gives her the option to choose payment frequency in each year from 1, 2, and 4. The frequency tells how many times the bank pays her the interests. Suppose there is no interest tax. a) How much Mary will get when the deposit matures after two years, when the interest payment frequencies per year are 1, 2, and 4 times, respectively? Which option is best for Mary? [5 marks] b) Former Chief Economist, John McDermott, in the Reserve Bank of New Zealand, says that inflation is a thief in your wallet. Suppose the inflation rate in New Zealand in the coming a few years is 2%. What are the real rates of returns of the annual bank deposit rate under the approximation rule, and in the exact relationship, respectively. [5 marks]