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6. Exponential functions are useful in business and economics. Power Point Lesson 7 discusses of the following: them. Show how the values are entered into your functions and also calculate the amounts of each al. You learn on the business channel that inflation was about 0.75% last month. Assume this rate is maintained each month for a year. What will the annualized rate be? EXAMPLE: A rate of 0.1% per month represents (1 + 0.001) 12 -1 = 0.0121 or 1.21% annually. ( It. 0075) 12-1 =. 0938or 9,38% annually a2. The value of your investment portfolio grew 8% last year. What average monthly growth rate was needed to achieve this 8% growth? EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)12. Solve this for r: r = 1.02 -1; r= .00165 or . 165% per month on average. 1.08 - (1 +r) 12 r=171 08 - 1 12 60643 or , 6435% . b1. F = Pen , which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r, expressed as a decimal) for the time (t, expressed in years) is given by the function. e is usually a key on a scientific calculator or it may be considered a constant approximately equal to 2.7183. EXAMPLE: If you invested $100 at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e(0.055)(6.25) = $100e(0.3438) = $100(1.4102) = $141.02. YOUR PROBLEM: Suppose you put $60000 in a savings account paying 4% per annum for 30 years for your retirement. What should your retirement account be worth after 30 years? F=60,000e (. 040)(30) F= $ 60,00De x(112) F= 60,000 X1.2 # 12.000 62. YOUR PROBLEM: You decide you need a nest egg of $500,000 by the time you retire in 30 years. If your retirement account earns 4.5%% annually, what amount does the formula P = Fle"t say you need to place in the savings account today in order to have the $500900 by the time you retire? EXAMPLE: A borrower tells you that he needs a loan for 6 years and 3 months and will pay you an annual rate of 5 1/2% for the loan, but will give you only $141.02 back at the end of the loan term , you should only loan him $100 today. $500,000 (415.4) $ 5001000 (627) $ 135,000 FunctionFandango 12.doc 081022