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Basic Mathematics for Economists phần 5

• tính toán kết hợp đầu ra tối đa hóa lợi nhuận của một chủ đề nhiều sản phẩm công ty hạn chế vào khả năng đầu vào, hoặc tính toán kết hợp đầu vào sẽ giảm thiểu chi phí tiêu chuẩn chất lượng tối thiểu được đáp ứng.Điều này làm cho nó trở thành một công cụ cực kỳ hữu ích | Solution A nominal annual rate of 47 corresponds to a 3-month rate of 47 -48 132 1.21875 As this rate is actually the discount on the maturity sum then the cost of 3-month Treasury Bills with redemption value of 100 000 of would be 100 000 1 - 0.0121875 98 781.25 and the amount of the discount is 1 218.75. Therefore the rate of return on the sum of 98 781.25 invested for 3 months is I 2 18 75 0.012338 1.2338 98 781.25 If this investment could be compounded for four 3-month periods at this quarterly rate of 1.2338 then the annual equivalent rate calculated using the standard formula would be AER 1.012338 4 - 1 1.050273 - 1 0.050273 5.0273 Test Yourself Exercise 7.2 1. If 40 000 is invested at a monthly rate of 1 what will it be worth after 9 months What is the corresponding AER 2. A sum of 450 000 is invested at a monthly interest rate of 0.6 . What will the final sum be after 18 months What is the corresponding AER 3. Which is the better investment for someone wishing to invest a sum of money for two years a an account which pays 0.9 monthly or b an account which pays 11 annually 4. If 1 600 is invested at a quarterly rate of interest of 4.5 what will the final sum be after 18 months What is the corresponding AER 5. How much interest is earned on 50 000 invested for three months at a nominal annual interest rate of 5 If money can be reinvested each quarter at the same rate what is the AER 6. If a credit card company charges 1.48 a month on any outstanding balance what APR is it charging 7. A building society pays an AER of 5.5 on an investment account calculated on a daily basis. What daily rate of interest will it pay 8. If 3-month government Treasury Bills are offered at an annual discount rate of 416 what would it cost to buy bills with redemption value of 500 000 What would the AER be for this investment 1993 2003 Mike Rosser 7.4 Time periods initial amounts and interest rates The formula for the final sum of an investment contains the four variables F A i and