Suppose you invest $250 at the end of each year for 10 years at an annual interest rate of r. The accumulated amount of money in your account after 10 years is given by 250((1 + r)¹⁰ − 1) - r A(r) = 1. Are there any values of r for which the function A is discontinuous? Why? = 2. How much money will you accumulate after 10 years if the interest rate is r = 0.01 (i.e., 1%)? If it is r = 0.10 (i.e., 10%)? 3. If your goal is to have $3500 in your account after 10 years, show that there is an interest rate r in the interval (0.01, 0.10) that allows you to reach your financial goal. (You do not need to find the interest rate.) Fully explain your reasoning.

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The price in dollars of a house during a period of mild inflation is described by the formula P(t)=96000e^0.05t where t is the number of years after 1990. Answer the following questions: A. The value of the house in the year 2000 will be  ___________ dollars. (Round your answer to the nearest dollar.)   B. In the year 2000 the value will be increasing at a rate of ____________ dollars per year. (Round your answer to the nearest dollar.)   C. How long will it take for a house to double in value? Answer: _____________ years. (Round your answer to two decimal places.)

If $1000 is invested at 7% compounded monthly, then the future value of the investment after x years is given by the functiony = 1000(1+0.07/12)^12x,x≥0Calculate:Future value of investment after 15 years =   Future value of investment after 14 years =  Future value of investment after 20 months =