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Actuarial Science
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Steven Kopp
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Lecture 2

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Western University

Actuarial Science

Actuarial Science 2053

Steven Kopp

Fall

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Chapter 1 Simple Interest and Discount DenitionsNotation P = principal = original amount borrowed = original amount invested I = interest = a dollar amount of money representing a fee or service charge paid to the lender for the use of hisher money we will assume that r>0 => I>0 r = rate of interest per year = ratio of the interest earned over a period of time to the principal t = length of investment (in years) S = accumulated value of P = original principle + interest Simple Interest (section 1.1) in any nancial transaction, there are two parties: the lender(investor) and the borrower(debtor) the debtor must pay back the original amount borrowed (at some point in the futire) along with a fee charged for the use of the money, called interest Interest: fee paid by the borrower, to the lender, for the use of the lenders money interest is calculated on the original principle only during the whole term of the investment (or loan), at the stated annual rate of interest it is calculated by means of the formula I = Prt from the denition of S, we have: S = P + I Time diagram: accumulated with interest combining the above two formulas, you get: S = P + I = P + Prt = P(1+rt) S = P(1+rt) Notes: the term (1+rt) is called the accumulation factor at simple interest 1. the process of calculating S from P is called he accumulation at simple interest 2.

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