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 0.25% 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. A power utility estimates that power consumption grew at an annual rate of 7% last year. What average monthly rate does this represent? Example: A 2% growth rate for the year would require 1.02 = (1 + r)¹². Solve this for ; r = .00165 which is 0.165% per month.

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. 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. If I deposit $10000 into my savings account that pays a 41/2% rate of interest per annum for 6 years and 3 months, what should I get back at maturity?  

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. Here is a loan proposition more in line with current interest rates. A borrower agrees to pay you 4% annually for 5 years and 6 months. At the end of the term, he will make a balloon payment of $20000 to repay the loan and the interest. What amount (P) does the formula P= F/e^rt  indicate you should loan this prospect?