Question 1 [10 marks] n-1 (a) Derive a recursive formula for the relationship between (la), and (Ta), Use this recursive formula to calculate (la) for n=1,2,...,30 at effective annual interest rates of i=0.1,0.2, ..., 1.0. [5] (b) A continuous cash flow stream starts with a payment rate of $10,000 for the first year and increases the rate by $500 each year from year 2 until year 15. The effective annual rate of interest is assumed to be 4% in the first 10 years and rising to 6% until the end of 15 years. Calculate the present value of this cash flow stream at time 0. [5] You may use the numerical results from part (a). Question 1 [10 marks] n-1 (a) Derive a recursive formula for the relationship between (la), and (Ta), Use this recursive formula to calculate (la) for n=1,2,...,30 at effective annual interest rates of i=0.1,0.2, ..., 1.0. [5] (b) A continuous cash flow stream starts with a payment rate of $10,000 for the first year and increases the rate by $500 each year from year 2 until year 15. The effective annual rate of interest is assumed to be 4% in the first 10 years and rising to 6% until the end of 15 years. Calculate the present value of this cash flow stream at time 0. [5] You may use the numerical results from part (a)