Reference no: EM132482319

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:

a1. You learn on the business channel that inflation was about 0.5% last month. Assume this rate is maintained each month for a year. What will be 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. In order for same store sales to contribute satisfactorily to earnings, same store sales need to grow about 5 1/2% per annum. What monthly growth rate is implied? EXAMPLE: A 2% growth rate for the year would require 1.02 = (1 + r)¹². Solve this for r = 1.0016515813019 - 1; r = .00165 or .165% per month on average.

b1. F = Pe^rt , 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. 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.  If you invest $15000 today, what amount does the formula say you will get back if you leave it for 5 years and 3 months in a savings account paying 4 1/2% annually?

b2. Alternatively, 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 , you should only loan him $100 today. The sports coup auto of your dreams will cost you about $45500. What amount do you need to invest today, P = F/e^rt , such that you will have $45500 in 12 years if you can earn 4 3/4% per annum on your money?