LrChVSICmpndIntrst - Math 131 Finite Mathematics. Dr. Raja...

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Math 131 Finite Mathematics. Dr. Raja Latif Chapter 5 Mathematics of Finance In this chapter we discuss mathematical methods and formulas that are 5.1 COMPOUND INTEREST OBJECTIVE: To ex- tend the notion of compound interest to include e/ective rates and to solve interest problems whose solutions re- quire logarithms. Compound Interest Formula S = P (1 + r ) n where r = i m = ( Annual interest rate ) ( Perids per year ) and n = mt; S = Compound amount (Accumulated amount at
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the end of n conversions); P = Principal; i = Nominal interest rate per year (annual interest rate); m = Number of compounding (conversion) periods per year; t = Term (number of years); n = Total number of compounding periods; r = interest rate per period. Derivation: First period: S 1 = P + rP = P (1 + r ) Second period: S 2 = S 1 (1 + r ) = [ P (1 + r )] (1 + r ) = P (1 + r ) 2 Third period: S 3 = S 2 (1 + r ) = h P (1 + r ) 2 i (1 + r ) = P (1 + r ) 3 ............................................. nth period: S n = S n 1 (1 + r ) = h P (1 + r ) n 1 i (1 + r ) = P (1 + r ) n :
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Example. B 131 Z: Compound Interest for Various Com- pounding Periods. If $ 1000 is invested at 8 % com- pounded ( A ) annuallly; ( B ) semiannually; ( C ) quarterly; ( D ) monthly: What is the amount after 5 years? Write answers to the nearest cent. Solution.
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LrChVSICmpndIntrst - Math 131 Finite Mathematics. Dr. Raja...

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