Nisha has a high paying job. She decides to make equal monthly deposits into a bank account, starting today, so that when she retires in 30 years she will present the savings from this bank account to a charity. The last deposit will be in exactly 30 years time. The money will then provide a perpetuity of annual payments to the charity with the first payment occurring in 31 years. Each payment will have the same purchase power as $3000 has today. The interest rate that she expects from the bank account is J4 = 4.147%, and the expected inflation rate is an effective 2% per year.

a. How much will Nisha need to have in her bank account in 30 years time to support the intended payments to the charity? [5]

b. How much must she deposit monthly to achieve her plan? [4]

c. What is the real rate of interest that she receives on her bank account?