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lecture3hout - MATH 006 Calculus and Linear Algebra(Lecture...

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MATH 006 Calculus and Linear Algebra (Lecture 3) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 16
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Outline 1 Future Value of an Annuity 2 Sinking Fund Albert Ku (HKUST) MATH 006 2 / 16
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Future Value of an Annuity Future Value of an Annuity Definition An annuity is a sequence of equal periodic payments. We call it an ordinary annuity if the payments are made at the end if each time interval. The amount, or future value , of an annuity is the sum of all payment plus all interest earned. Remark In this course, all annuities are assumed to be ordinary. Albert Ku (HKUST) MATH 006 3 / 16
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Future Value of an Annuity An Example Example Suppose you deposit $100 every 6 months into an account that pay 6% compounded semiannually. If you make six deposits, one at the end of each interest payment period, over 3 years, how much money will be in the account after the last deposit is made? Albert Ku (HKUST) MATH 006 4 / 16
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Future Value of an Annuity Solution Idea: We compute the future value of each payment one by one and then sum them up. Future value of the 1st payment: 100(1 + 0 . 06 2 ) 5 Future value of the 2nd payment: 100(1 + 0 . 06 2 ) 4 Future value of the 3rd payment: 100(1 + 0 . 06 2 ) 3 · · · · · · Future value of the 6th payment: 100 Albert Ku (HKUST) MATH 006 5 / 16
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