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by: jin soo kim

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# MA 373 Intro and Simple Interest MA 37300

Marketplace > Purdue University > Mathematics (M) > MA 37300 > MA 373 Intro and Simple Interest
jin soo kim
Purdue

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Just notes from class
COURSE
Financial Mathematics
PROF.
Jeffrey A. Beckley
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
Financial math
KARMA
Free

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by jin soo kim on Sunday March 13, 2016. The Class Notes belongs to MA 37300 at Purdue University taught by Jeffrey A. Beckley in Fall 2016. Since its upload, it has received 45 views. For similar materials see Financial Mathematics in Mathematics (M) at Purdue University.

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Date Created: 03/13/16
MA 373 NOTES Non­interest Theory Facts 1. Sum of an Arithmetic Sequence = ((1  Term + Last Term) / 2) * (# of terms) Ex. 4 + 7 + 10 + 13 + 16 + 19 = ((4 + 19) / 2) * (6) = 69 2. Sum of Geometric Series = (First Term – Next Term after the last term) / (1­ Ratio)   2 3 n  n+1) Ex. 1 + s+ s  + s  + … + s = (1 – s   / (1 – s) 2   1/2 3. Quadratic Equation:   x = (­b ± (b – 4ac)  ) / (2a) 4. A  – B = (A – B) (A + B) 5. (ax + b) * (ax + b) = a x  + 2abx + b 2 2 2 2 6. (ax ­ b) * (ax ­ b) = a x  ­ 2abx + b Introduction to Simple Interest K                                                                                                                                           S = A(t) |­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­| 0                                                                                                                                                     t    k = Principle (Amount we Invest/Borrow) S ­ K = interest  t= Time Definitions A kt) = Amount function for principle K A(t) = Amount at time t if we have K at time zero a(t) = Accumulation function = A (t) = amount at time t if we have 1 time 0. 1 Properties A(0) = K a(0) = 1 K                                 1(t )                                               2         A(t )                                         |­­­­­­­­­­­­­­­­­­­­­­­­­­­­­|­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­|­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­| 0                                1    t                                              2                t                           Amount of interest for the interval of t  to t  = 1(t ) 2 A(t ) 2 1 Effective interest rate for t1 to t2 = (a(t ) – a(t2)) / a(1 ) 1 A(t) = k * a(t) = (k*a(t ) – k2a(t )) / (k1a(t )) 1 Effective interest rate for the n  period = i  = (a(n) n a(n ­ 1)) / a(n ­ 1) By rearranging, a(n) =a * (n ­ 1) * (a + i ) n Simple Interest: a(t) = 1 + S * t, where S = simple interest and t = time *THIS ONLY WORKS FOR SIMPLE INTEREST S    In = (a(n) – a(n – 1)) / (a(n ­ 1)) = (1 + S  – [1 n S(n­1)]) / (1 + S[n­1]) =     1 + S*(n - 1)

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