HW 12 Solutions

HW 12 Solutions - Exponential and Logarithmic Functions...

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Exponential and Logarithmic Functions Homework Solutions STOR 112 Throughout, we use r to be the interest rate, n to be the number of compoundings per time period, and t to be the number of time periods. The general formula for compound interest is P ± 1 + r n ² nt where P is the amount of money we start with. The general formula for continuously compounded interest is Pe rt where P is the amount of money we start with. 1. You invest a dollar in a stock. Suppose that (a) the stock appreciates 20% , then depreciates x % , and as a result, you will have your money back exactly, i.e. 1$. What is the value of x ? First, remember that if the rate is x % then r = 0 . 01 x (for example, when the rate is 20% then r = 0 . 20). Then after the appreciation we will have 1 . 20, and after the depreciation we will have 1 . 20(1 - 0 . 01 x ). But this is exactly 1, so solve for x : 1 . 20(1 - 0 . 01 x ) = 1 which gives x = 16 . 6667%. (b) the stock depreciates x % , then appreciates 20% , and as a result, you will have your money back exactly, i.e. 1$. What is the value of x ? Here, we will have (1
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HW 12 Solutions - Exponential and Logarithmic Functions...

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