MATH 2FM3 Lecture Notes - Lecture 1: Growth Factor, Financial Transaction, Investment
22 Oct 2015
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1. 1 interest accumulation and e ective rates of interest: in general interest rate is computed annually. At the end of the year the interest is paid or reinvested. If reinvested it leads to compounding interest (more interest): example: you deposit 1000$ into a saving account with 9% interest per annum. Assuming no transactions on the account, determine the account balance after 3 years. Solution: after 1 year the interest is 1000 0. 09 = 90 resulting in balance. 1000 + 1000 0. 09 = 1000 1. 09. 1000 1. 09 + 1000 1. 09 0. 09 = 1000 1. 09 (1 + 0. 09) = 1000 (1. 09)2. 1000 (1. 09)2 + 1000 (1. 09)2 0. 09 = 1000 (1. 09)2 (1 + 0. 09) = 0: from this example we see a pattern of interest accumulation which leads to the following theorem, theorem: a deposit c with interest i per annum will accumulate to c(1 + i)n after n years.
, without using addition, only one instance of each function and the same value of x.
