Provide solutions to the following questions.
Q.1) (i) An insurance company earned a simple rate of interest of 8% over the last calendar year based on the following information: Item Rs. Assets, beginning of year 25,000.000 Sales revenue X Net investment income 2,000,000 Salaries paid 2,200,000 Other expenses paid 750,000 All cash flows occur at the middle of the year. Calculate the effective yield rate. (3) (11) Fill in the blanks: (a) Two factors that might influence the level of interest rates are the likelihood of on payments and the possible or of currency. (1) (b) The calculation of the amount of interest payable under a financial arrangement can be expressed in terms of or (1) (iii) To accumulate Rs.8000/- at the end of 3n years, deposits of Rs.98/- are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i . You are given (1 + i)" = 2.0. Determine i. (2)4 points) Describe how each of the following regulatory incentives can promote counter-cyclicality of funding rules for defined benefit pension plans: (i) Avoid excess reliance on current market values (ii) Allow appropriate levels of overfunding through flexible tax ceilings (iii) Limit contribution holidays and access to surplus (iv) Encourage stability of long-term contribution patterns through appropriate actuarial methods3.C. [0.5 points] Using some more sophisticated programming, and assuming y = 0.25, we are able to calculate that "* = 67 and A(7"*) = 3, 010. Assume that any NPV values calculated reflect returns for a single acre of forest. We also know the forest stand in question is located in a region where the NPV of con- tinuous returns to agricultural land use are NPVa, = 8, 000 per acre. Assuming the forest stand is currently bare land, and using the same parameters from Problem 2.B, would the landowner choose forest land use over agriculture without the carbon rental payment (Hint: calculate NPVP(T))? With the carbon rental payment (Hint: calculate NPV* (T*))? 3.D. Again, assume we have found T* = 67. Instead of issuing carbon rental payments, the government decides it would like to achieve the same socially optimal T* by introducing a severance tax on timber, which imposes a per-unit volume cost of w on timber harvest. This means that the private net-present- value of all forest rotations is now: NPV* = -D+ >e-(T) [(p-w)Q(T) -D] 1= 1 = -D+ (p - w)Q(T) - D erT - 1 i) [1 point] What value should the government set w to achieve T*? Assume the government is con- sidering three different values for w: 0.5, 0.75, 0.98. Use Excel to determine which one gets the closest to achieving the socially-optimal rotation interval 7". Use the same parameter values as for Problem 2.B. ii) [0.5 points] Suppose the government will pick the severance tax value that gets the closest to achiev- ing the socially-optimal rotation interval 7*. Assuming the forest stand is currently bare land, would the landowner choose the forest land use over agriculture? Based on your answer, do you think the severance 3 tax will achieve the same objective as the carbon rental payment of increasing total forest carbon stock (over many acres)? Why or why not?Which of the following criteria is a necessary and sufcient condition for the sample variance, dened as .52 =[2Xnf2], of a set of n observations from a population to be an unbiased estimator of the population variance? a 33 will always be unbiased. B S2 will be unbiased if and only if the observations are independent. C .25;2 will be unbiased if and only if the observations are normally distributed. D S2 will be unbiased if and only if the observations are independent and normally distributed. [3]
