kindly help in solving the following questions clearly explaining your answers.

A training company is planning to expand into another country. The set up costs (which are paid out at the start) are expected to be $50,000. Rent and salaries totalling $120,000 pa are to be paid monthly in arrears for the first two years. After two years, the total monthly payment for rent and salaries increases each month by $100. The expected sales of courses and materials during the first three years of business are shown in the table below: Year Total income from Total income from sales of materials sale of courses $40,000 $20,000 $120,000 $120,000 3 $140,000 $160,000 The income is to be payable monthly in advance but, in the first year, no income is received until the beginning of the 8th month. After the first three years, sales of both materials and courses are expected to grow at a rate of 0.5% per month compound. (i) Assuming that the business continues indefinitely, calculate the net present value of this project at an effective rate of interest of 8% pa. [7] (ii) Show that the discounted payback period for the project, at an effective rate of 8% pa, is less than 2 years. Hence calculate the discounted payback period. [5] (iii) Calculate the accumulated profit for this project after 5 years, using an annual effective rate of interest of 8% pa. [3] (iv) A year after setting up the project, it is sold. The original investors earned an effective annual rate of return of 9% pa. Calculate the sale price. [4] [Total 19]A discrete random variable has a probability function given by: 2 4 P(X = x) $+2ax 2-30 3+ a (i) Give the range of possible values for the unknown parameter of. [1] A random sample of 30 observations gave respective frequencies of 7, 6 and 17. (ii) Calculate the method of moments estimator of o. (3] (iii) Write down an expression for the likelihood of these data and hence show that the maximum likelihood estimate o satisfies the quadratic equation: 111 91 180a- + =0 [5] 32 (iv) Hence determine the maximum likelihood estimate and explain why the second root is rejected as a possible estimate of o. [3] [Total 12]