Exponential functions are useful in business and economics. Lesson 7 discusses t

Question

Exponential functions are useful in business and economics. Lesson 7 discusses them. Show how the values are entered into your functions and also calculate the amounts of each of the following:

            a. You learn on the business channel that inflation was about 1.1% 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.

            b. F = Pert 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), in years is given by the function. Thus 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.   Here is a CD offer more in line with current rates. You have $2500 to invest. The bank will pay you 0.25% per annum. If you place your money for 39 months in this CD, what do you expect to get back at the end of the time?

Explanation / Answer

(a)

Annualized rate = (1 + 0.011)12 - 1 = (1.011)12 - 1 = 1.1403 - 1 = 0.1403, or 14.03%

(b)

Future value ($) = 2,500 x e(0.0025) x 3.25 = 2,500 x e0.0081 = 2,500 x 1.0081 = 2,520.33

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