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 for
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 for each of the following:
a1. You learn on the business channel that inflation was about 0.3% 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.
a2.You are trying to manage expenses, and decide that you will allow them to grow only 7% this year.Assuming you want a level (the same) monthly growth rate for each month, what will be the monthly growth rate that the 7% annual rate allows?EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)12.Solve this for r:; r = .00165 or .165% per month on average.
b1.F = Pert,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), in years is given by the function.EXAMPLE:invest $100 at the annual rate of 5 1/2% for 6 years and 3 months and you should 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 $5500 to invest.The bank will pay you 0.45% per annum.If you place your money for 1 year 6 months in this CD, what do you expect to get back at the end of the period?
b2.Alternatively, P = F/ert.P tells you the most you should loan or the most you need now to save to meet future goal F.Thus, if 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, youshouldonly loan him $100 today.In 6 years you plan to spend $35500 on a new car.Assuming you can earn 3 1/2% annually on your savings, what amount do you need to save today to meet your goal 6 years hence?
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