Address all questions appropriately.

An investor is considering making an investment in one or both of two projects. The cashflows associated with the projects are as follows. The unit of time is years. Project A: Initial payments of $2 million at time zero and f4 million at time 2 are made. In return a sum of 1900,000 per annum is paid continuously from time 5 to time 25. Project B: Regular payments of $100,000 are made at the start of each year for 10 years. In return, amounts of X, 2X, 3.X and so on are made annually for 10 years, the first payment being made at time 1 1. (i) Find the net present value of Project A at an effective annual interest rate of 10% [2] (ii) Show that the internal rate of return for Project A is 9.38% pa. [2] (iii) Find the value of X if the internal rate of return for Project B is the same as that for Project A. [3] (iv) Find the value of X" if both projects are to have the same net present value at 10% pa. [3] (v) The investor proposes to borrow all the money needed for the project. Funds are available at an interest rate of 7% per annum effective. Repayments can be made at any time, and positive cash balances can be invested to yield 3% per annum. If X = $45,000, find the accumulated value of each project at the end of the 25 year period. [12] [Total 22]In a one-year investigation of claim frequencies for a particular category of motorists, there were 150 claims from the 500 policyholders aged under 25 and 650 claims from the 4,500 remaining policyholders. Assuming that the numbers of claims made by the individual motorists in each category have Poisson distributions, calculate a 99% confidence interval for the difference between the two Poisson parameters