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School

Western University
Department

Actuarial Science

Course Code

Actuarial Science 2053

Professor

Steven Kopp

Lecture

2

Chapter 1- Simple Interest and Discount!

!

Deﬁnitions/Notation!

!

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

his/her money!

!

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 ﬁnancial 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 lender's 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 deﬁnition of S, we have:!•

S = P + I!‣

Time diagram:!◦

!

!

!

!

!

!

!

!

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.

we will assume that r>0 => I>0•

accumulated with!

$interest

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