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CALCULUS 2 (BA) Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai Department of mathematics INTERNATIONAL UNIVERSITY, VNU-HCM February 25, 2014 Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) References Main textbook: M. L. Lial, R. N. Greenwell, N. P. Ritchey Calculus with Applications, 10ed. Pearson, Boston, 2012. Other textbooks: L. D. Hoﬀmann, G. L. Bradley, Calculus, Brief 10ed. McGraw-Hill, Boston, 2010. Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Chapter 1 . Mathematics of Finance Contents 1. Compound Interest 2. Continuous Money Flow: Total money ﬂow, present value, accumulated amount of money, continuous…show more content…
So the answer is “almost”. Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Compound interest Example 1.3 What principal is required now so that after 6 years at a rate of interest of 5 per cent p.a. the ﬁnal amount is 20, 000 EUR? Solution It follows from Equation 1 that A P= . (1 + i)t Substituting t = 6, i = 0.05 and A = 20, 000, we obtain A 20, 000 P= = = 14, 924.31 EUR 6 (1 + i) (1 + 0.05)6 i.e., the principal required now is equal to 14, 924.31 EUR. Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Compound interest Part year investment Often, we do not have an annual period for interest payments, i.e. compounding takes place several times per year, e.g., • semi-annually–there are 2 interest payments per year, namely after every six months; • quarterly–there are 4 payments per year, namely one after every three months; • monthly–there are 12 payments, namely one per month; • daily–compounding takes place 360 times per year. Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc Hai CALCULUS 2 (BA) Compound interest If the annual interest rate is r and there are n interest payments per year, the rate of interest per payment period is equal to j = r /n, and the number of interest payments within a period of t years is equal to tn. Denoting by A(t) the amount at the end of t years with n interest payments per year, formula (1) changes into A(t) = P (1 + j)nt Assoc. Prof. Nguyen Dinh Dr. Nguyen Ngoc