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lecture2hout - MATH 006 Calculus and Linear Algebra...

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MATH 006 Calculus and Linear Algebra (Lecture 2) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 17
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Outline 1 Compound Interest 2 Annual Percentage Yield Albert Ku (HKUST) MATH 006 2 / 17
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Compound Interest Compound Interest Example If $1,000 is deposited at annual interest rate 10% and the bank provides interest (a) annually; (b) semiannually; (c) quarterly; (d) monthly. What is the amount of money in the bank after 4 years? Albert Ku (HKUST) MATH 006 3 / 17
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Compound Interest Solution for (a) Amount of money in the bank at the end of the 1st year: 1000(1 + 0 . 1) Amount of money in the bank at the end of the 2nd year: 1000(1 + 0 . 1)(1 + 0 . 1) = 1000(1 + 0 . 1) 2 Amount of money in the bank at the end of the 3rd year: 1000(1 + 0 . 1) 2 (1 + 0 . 1) = 1000(1 + 0 . 1) 3 Amount of money in the bank at the end of the 4th year: 1000(1 + 0 . 1) 3 (1 + 0 . 1) = 1000(1 + 0 . 1) 4 = $1464 . 1 Albert Ku (HKUST) MATH 006 4 / 17
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Compound Interest Solution for (b) The computation is similar to the solution for (a). But now the period of providing interest is half year. Therefore, we have the following: Amount of money in the bank at the end of the 1st half-year: 1000(1 + 0 . 1 2 ) Amount of money in the bank at the end of the 2nd half-year: 1000(1 + 0 . 1 2 )(1 + 0 . 1 2 ) = 1000(1 + 0 . 1 2 ) 2 ······ Amount of money in the bank at the end of the 8th half-year: 1000(1 + 0 . 1 2 ) 8 = $1477 . 5 Albert Ku (HKUST) MATH 006 5 / 17
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lecture2hout - MATH 006 Calculus and Linear Algebra...

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