please solve on page only part a

\f1. In this question any Greek letters 01,5, 7, 6, 6 refer to the digits of your student number, as described in the instructions on the second page of the exam. a. Suppose that you deposit 100(1 + 0:) pounds in an account that gives an annual interest rate of r = (1 + 10/ 100. Under an annual compounding convention, calculate the minimum number of years (your answer should be an integer) it would take for the bank balance to exceed 1000(2 + ,3) pounds. [5 marks] b. Suppose that starting one year from now, you will receive 100(1-l 'y) at yearly intervals, until 10 + 6 payments have been made to you. Assuming an annual interest rate of 1' = (1 + 6)/ 100, work out the present value of the cashow. [5 marks] 0. A generous individual has donated 20000 + 700(1 + a) to a bank account in a museum's name. At yearly intervals, starting one year from now, .6500 is removed from the bank account to fund museum activities, but at the precisely the same times interest is added according to an annual interest rate 0.01. (i) Work out an expression for how much money is in the bank account after T years, expressed as a function of T. You may assume that T is not large enough to make the bank account balance negative. (ii) How many times will the museum be able to withdraw .8 500 before the money left decreases to less than 500? [10 marks]