# math - Quarterly: m=4 Monthly: m=12 Semi annually: m=2...

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Quarterly: m=4 Monthly: m=12 Semi annually: m=2 Annually: m=1 n= whole time of the long- m=payment every years “Simple interest” (I=Prt)-Future value (A(t)=P+Prt) “Arithmetic Sequence” – first term (a 1 )-common different (d)- a n =a 1 +(n-1)d Sum of first n terms of an arithmetic sequence S n =n/2 (a 1 +a n ) “Geometric sequence”-n term of geometric sequence is: a n =a 1 r n-1 The sum S n of 1 st n terms of a geometric sequence: S n =a 1 (r n -1)/(r-1) If P is invested at interested rate r compounded m times per years: A(t)=future value=P(1+r/m) mt Rate per compounding period= i=r/m ---- number of compounding period=n=mt Compounding continuously= A(t)=Pe rt Present value=how much need to be invested today (P) to reach a goal of \$A in t years= A(1+r/m) -mt or A(1+i) -n -Continuously P=Ae -rt +How much \$ today will be \$100,000 in 20 years? Compounded continuously is more effective than quarterly and quarterly is more effective than annually Effective rate for compounding m times per years= r=(1+r/m)

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## This note was uploaded on 12/16/2009 for the course MATH MATH 106 taught by Professor Mcarthur during the Spring '09 term at Aarhus Universitet.

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math - Quarterly: m=4 Monthly: m=12 Semi annually: m=2...

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