Actuarial Science 2553A/B Lecture Notes - Lecture 2: Interest
11 Oct 2016
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Document Summary
There are many different functional forms of the accumulation function, a(t) However, there are two functions that are used most often in the financial world. These two functions represent two different types of interest calculation: simple interest (section 1. 3, compound interest (section 1. 4) Interest is calculated only on the original principal during the whole term of the investment (or loan), at the stated annual rate of interest; there is no interest earned on any interest that is paid. That means the interest earned is the same each period: We know that i = s p. S = p + i = p + p i t. In other words: a(t) = 1 + i t accumulation function. A(t) = a(0)[1 + it] = p[1 + it] amount. Notes: the term (1 + it ) is called the accumulation factor at simple interest, the process of calculating a(t) from p is called accumulation at simple interest.
