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HW 11 Solutions

# HW 11 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 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. How much money will you have, if (a) The stock appreciates 20% , then depreciates 20% ? First the stock appreciates 20%. So n = 1 and r = 0 . 20. Then we will have 1(1 + 0 . 20) = 1 . 20 dollars Next the stock depreciates 20% . So n = 1 and r = - 0 . 20. Then we will have 1 . 20(1 - 0 . 20) = 1 . 20 · 0 . 80 = 0 . 96 dollars (b) The stock depreciates 20% , then apppreciates 20% ? First, the depreciation: 1(1 - 0 . 20) = 0 . 80 dollars Then, the appreciation: 0 . 80(1 + 0 . 20) = 0 . 80 · 1 . 20 = 0 . 96 dollars (c) The stock appreciates 20% , for each of 5 consecutive years, then depre- ciates 20% for each of 5 consecutive years ?

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