Section1.123(2)

# Section1.123(2) - Chapter 1 Simple Interest and Discount Simple Interest(section 1.1 Consider the following transaction Person A lends money to

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Chapter 1 – Simple Interest and Discount Simple Interest (section 1.1) Consider the following transaction: Person A lends money to person B person A is called the “lender” or “investor” person B is called the “borrower” or “debtor” the debtor must pay back the original amount borrowed (at some point in the future) along with a fee charged for the use of the money, called interest

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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
Simple Interest Interest is calculated on the original principal 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 = P r t From the definition of S, we have: S = P + I

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Combining the above two formulas, you get: S = P + I = P + Prt = P ( 1 + rt ) S = P (1 + rt )
Note About Time The value of t must be given in years If time is given as something other than years, we make the following adjustments to t : 1. If time is given in months, then 12 months of number t = 2. If time is given in days, or if you are given actual dates, then (a) Exact Interest: 365 days of number t = (b) Ordinary Interest: 360 days of number t =

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Example 1.1.1 Using exact and ordinary interest, what will \$1000 accumulate to over 120 days at r = 7%? Solution to 1.1.1
Example 1.1.2 You invest \$5000 in a 6-month guaranteed investment certificate (GIC) paying interest at r = 4%. (a) What is the maturity value of the GIC? (b) What is the maturity value of the GIC if you invested the money on May 7, 2009? Solution to 1.1.2

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Example 1.1.3 How long will it take \$1500 to earn \$22.50 interest at r = 9%? Solution to 1.1.3
Suppose you bought some furniture for \$977 and paid “no interest for 90 days”. However, there was a \$25 administration charge to be paid up front. What interest rate were you charged for this “no interest” payment plan? Solution to 1.1.4

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## This note was uploaded on 04/14/2010 for the course ACSCI 2053 taught by Professor Kopp during the Spring '09 term at UWO.

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Section1.123(2) - Chapter 1 Simple Interest and Discount Simple Interest(section 1.1 Consider the following transaction Person A lends money to

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