.Solve the following attachments.

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)A. professional gambler has said: \"Flipping a coin into 1e air is fair, since the coin rotates about a horizontal axis, and it is equally likely to be either way up when it rst clips the ground. So a flicked coin is equally likely to land showing heads or tails. However, squirming a coin on a table is not fair, since the coin rotates about a vertical axis, and there is a systematic bias causing it to tilt towards the side where the embossed pattern is heavier. In fa:t, when a new coin is spun, it is more than twice as likely to land showing tails as it is to land showing heais." After hearing this, you carried out an experiment, spinning a new coin 25 times on a polished table, and found that it showed tails 13 times. Do the results of your experiment support the gambler's claims about the probabilities when a coin is spun? [3] The demand and supply equations for the apple market are: Demand: P - 12 - 0.010 Supply: P = 0.02Q where P- price per bushel, and Q-quantity. (Drawing graphs will help you a lot!) a. Calculate the equilibrium price and quantity. b. What are the consumer surplus and the producer surplus at the market equilibrium? c. Suppose the government imposes a price floor of 10 TL for apples. Calculate the consumer and producer surpluses after the price floor is applied. What is the dead weight loss resulting from this policy?2. Algebraic manipulation example In this next set of exercises, we are going to prove a useful statement in two ways: first by using the real-valued trigonometric functions, and next by using the complex-exponential representation of the same trigonometric functions. This exercise will serve to show the close relationship between complex exponential functions and trigonometric functions. Following is a true general statement regarding periodic oscillations: A periodic oscillation at angular frequency w can be represented in general by f(t) = A cos(wt + (), where A represents the amplitude and o represents the phase factor. This same periodic oscillation can be represented by f(t) = Bcos(wt) + C sin(wt) for an appropriately chosen constants B and C. In other words, f(t) = A cos(wt + $) = Bcos(wt) + Csin(wt) and we will come up with formulas for B and C in terms of A and @ and prove this statement in the next set of exercises, starting with the first method using real-valued trigonometric functions. a. First method: The strategy here is to expand out the left-hand side (A cos(wt + ) ) using the angle addition formula. Using one of the angle addition formulas, expand out the left-hand side and fill in the blanks below (watch out for signs). A cos(wt + p) = A( cos(wt) + [Format Hint: (1) Use "*","+","-", and "/" for multiplication, addition, subtraction, and division. (2) Spell out Greek letters (e.g. "omega" for w). (3) Use the usual name for functions ("sin", "cos", "tan", etc.).] b. For this equality to hold for all time t, the coefficients to the cos(wt) terms on left- and right- hand sides should be equal to each other, and the coefficients to the sin(wt) terms on left- and right-hand sides should be equal to each other. We call this "collecting like terms" or "comparing like terms" (remember the phrase "like terms" from algebra?). Fill in the blanks below by comparing like terms: B = , and C =