Exponential_and_Reciprocal_Functions

Marshall 6.26 a, b, c, and d only Using a present value table, your calculator, or a computer program present value function, answer the following questions: Microsoft Excel's Present Value function was used to answer these questions. a. What is the present value of nine annual cash payments of $4,000, to be paid at the end of each year using an interest rate of 6%' ANSWER: The present value of nine annual cash payments of $4,000 paid over a nine year period (totaling $36,000), at an interest rate of %6 is $27,206.77. b. What is the present value of $15,000 to be paid at the end of 20 years, using an interest rate of 18%' ANSWER: The present value of $15,000 at the end of a 20 year period with an interest rate of 18% would be $547.58. c. How much cash must be deposited in a savings account as a single amount in order to accumulate $300,000 at the end of 12 years, assuming that the accounting will earn 10% interest' ANSWER: The one time amount to be deposited into a savings account, to accumulate $300,000 at the end of a 12 year period with an interest rate of 10% would be $95,590.00 d. How much cash must be deposited in a savings account (as a single amount) in order to accumulate $50,000 at the end of seven years, assuming that the account will earn 12% interest' ANSWER: The one time amount to be deposited into a savings accounting, to accumulate $50,000 at the end of a 7 year period with an interest rate of 10% would be $22.616.00. Sevilla Topic 6, Exploration 8b Consider the formula P = 67.38 x(1.026)t. If we let P represent the population of Mexico in year t where t is the number of years from 1980, confirm that this formula gives the same population values as those given in the table in Example 6.5. a. Explain where the number 67.38 and the number 1.026 were obtained. ANSWER: The formula for present value is used: fv = pv * (1+i)^n, where fv = future value; pv = present value; i = the increase rate (percentage of growth); and n = the number of periods. With this in mind the number 67.38 (from the table above) was obtained as the present value (1980's). The number 1.026 was obtained by determining the growth rate, in this case 2.6%. b. What would the population in 1990 have been if growth had continued in this same pattern' ANSWER: The population in 1990 would have been 87.10 if the growth had continued with a 2.6% increase. p = 67.38 * (1.026)^11 = 67.38 * 1.293 = 87.10 McConnell Chapter 8, Study Questions 1 and 2 1. Why is economic growth important' Why could the different between a 2.5 percent and a 3 percent annual growth rate be of great significance over several decades' ANSWER: Economic growth is important because it shows a sign of strength, which usually wields favorable to the people as growth means better wages and better living conditions. Good economic growth can lower poverty, increase public services and mean more spending by the people with little or no taxes increases. As the reading this question stated "for the United States, with a current real GDP of about $10.5 trillion, the difference between a 3% and a 4% rate of growth is about $105 billion..." (McConnell, 2005, p. 132) This can make a huge difference to annual budget. 2. Suppose an economy's real GDP is $30,000 in year 1 and $31,200 in year 2. What is the growth rate of its real GDP' Assume that the population is 100 in year 1 and 102 in year 2. What is the growth rate of GDP per capita' ANSWER: The real GDP growth rate for an economy in year 1 with a real GDP of 30000 and year 2 31200 would be 4%. The growth rate of the GDP per capita with year 1 having a total population of 100 and year 2 102 would be 1.96%.