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07_Practice_Key - MAC 1147 Quiz#7 Practice Name Key For...

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MAC 1147 - Quiz #7 Practice Name: Key For full credit, you must show all work and circle your final answer. 1 The interest rate for a bank account is 7.5%. Find the annual percentage yield if interest is compounded: (2 points) (a) Weekly (b) Continuously [Note: “Annual Percentage Yield” (APY) means the actual percentage rate you’ll get. For example, if interest is only compounded once per year, the APY is the same as the interest rate.] Y = 1 + . 075 52 52 · 1 1 . 077826 . So, APY 7 . 7826%. Y = e . 075 · 1 1 . 077884 . So, APY 7 . 7884%. 2 A poor graduate student deposits $100 into his bank account. (2 points) (a) If he has an interest rate of 4%, and his interest is compounded monthly, how many months will it take for his money to double? (b) If his interest is compounded continuously and his money doubles in 10 years, what was his yearly interest rate? 2 = 1 + . 04 12 12 · t ln 2 = 12 t ln 1 + . 04 12 t = ln 2 12 ln 1 + . 04 12 t 17 . 358 months t = 18 months. 2 = e r · 10 ln 2 = ln ( e 10 r ) ln 2 = 10 r r = 1 10 ln 2 r . 06931 r 6 . 931% . 3 Assume that the number of cups of coffee a graduate student drinks each day increases exponentially. On the first day, he drinks 2 cups of coffee. On the fifth day, he drinks 20 cups of coffee. Find the
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