3. At time 0, deposits of 10,000 are made into each of Fund X and Fund Y. Fund X accumulates at an annual effective interest rate of 5%. Fund Y accumulates at a simple interest rate of 8%. At time t, the forces of interest on the two funds are equal. At time t, the accumulated value of Fund Y is greater than the accumulated value of Fund X by Z. Determine Z. 4. (i) At time t =0, Donald puts 1,000 into a fund crediting interest at a nominal rate of i compounded semiannually. (ii) At time t = 2, Lewis puts 1,000 into a different fund crediting interest at a force of = , for all t. way he gummed add do Y (61) (iii) At time t = 16, the amounts in each fund will be equal. Calculate i. 5. Carl puts 10,000 into a bank account that pays an annual effective interest rate of 4% for ten years. If a withdrawal is made during the first five and one-half years, a penalty of 5% of the withdrawal amount is made. Carl withdraws K at the end of each of years 4.5.6, and 7. The balance in the account at the end of year 10 is 10,000. Calculate K.19:35 Gal pal 100% June_BM_A_II.pdf Q.2. (A) Madam Dora purchased a TV set for $550 and later decided to sell for $600. She sold it under the following hire purchase terms. An initial payment of 30% of the price and the balance paid in monthly equal installment at 10% simple interest per annum for 2 year. i. Calculate the amount paid every month ii Calculate the amount the buyer paid for the TV set. [3] ifi. Calculate the percentage profit Madam Dora made on the cost price of the TV set. (B) An investment requires an initial payment of 10,000 cedis and annual payments of 1000 [7] cedis at the end of each year of the years. Starting at the end of the eleventh year, the investment returns five equal annual payments of X. Determine the value of X to yield an annual effective rate interest over the 15-year period. (C) Let R denote a fixed regular payment made at the beginning of each year for a years. If R is invested at annual effective interest rate of i,"'""" " '\"'\""""' ---...........- I." \"""'" ""1 Consider a Diamond model, where we set the productivity factor A; to unity (1) in all periods. The working population, Lg, grows at rate R, i. e., Li\": (1 + n)L. Lower-case letters denote perworker terms, e.g. k, = K,/L,. Agents live for tam periods. Income earned (from labor) in the rst period of life (10,) is spent on saving (3,) and rstperiod consumption (Cu). The rst-period budget constraint can thus be written 011 = to: ' 31. In retirement, the same agent consumes 02,\3. The IS-LMFE Model. Consider a closed eoonomy where desired consump- tion is given by: Cd = 1m + car 1cm? Desired investment is described by: I? = 50 lr Government purchases are equal to G = 2st}. The liquidity function is: MY, 2') = 1m + 0.2? 25an Assume that M = 5m}, P = 1'0 and an"! = H.132. 3} b} 8} Derive the IS Curve for this economy. Plot it on a diagram with Y on the horizontal axis and r on the vertical axis. Derive the LM curve. Plot on your diagram from part a). Solve for the equilibrium levels of r and Y in this economy. What must full employment output be in order for this to be a. general equilibrium? Plot the FE curve on your graph and label the equilibrium. Show the effects of an expansionary scal policy by deriving the IS Curve in the case where {3\" = 3013. Plot it on your graph. What are the new levels for r and 1"? Is the economy in a. long run equilibrium? What is another example of a factor that may shift the IS Curve other than scal policy? Be sure to note the direction the IS Curve will shift. Show the elfects of a contractionary monetary policy by deriving the LM Curve in the case where M\" = 5!]. Plot it on your graph. What are the new levels for r and Y? What is another example of a factor that may shift the LM Curve other than the nominal money supply? Be sure to note the direction the LM ICurve will shift. In this question, work with the original IS curve from part a]
