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20.2 Simple Interest

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The simplest type of interest is called SIMPLE INTEREST If you borrow money, you must pay for the use of that money. If you lend money, you will be paid for the use of that money. The price of borrowing or lending money is called interest.

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Simple Interest is the interest (I) paid on an investment or loan on the basis of the original amount invested or borrowed, which is called the principal (P). The amount of the simple interest is constant from year to year and is therefore linearly related to the term of the investment (t).

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Example: Suppose you borrowed $500 from a friend and agreed to pay back the loan with 10% interest per annum. How much would you have to pay your friend after 2 years? Solution: 1. Calculate the interest owed after one year. Interest = 500 x 10_ = $50 100 2. Calculate the interest owed after the second year. Interest = 500 x 10_ = $50 100

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3. Calculate the total interest. $50 + $50 = $100 4. Add the amount borrowed to the interest to calculate the funds due to be repaid. $500 + $100 = $600 This method is known as calculating simple interest from first principles. Since the amount of simple interest earned is the same every year, we can apply a general rule.

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To calculate the simple interest earned or paid use the rule: I = Prt__ 100 where P = amount invested or borrowed r = interest rate per year t = is the time in years

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Total Amount, A, of an investment The amount of an investment, A, is the principal plus the amount of interest earned. A = P + I = P + Prt_ 100 Here, P is the amount invested or borrowed, r is the interest rate and t is time (in years).

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Calculating the simple interest for a period other than one year. If the money is invested/borrowed for more or less than one year, then t needs to be adjusted accordingly. Example: How much interest would be due on a loan of $5000 at 10% per annum for six months? Solution: P= 5000 r=10% t= 6_ 12 I = Prt = 5000 x 10 x (0.5) 100 100 I = $250

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The formula given for simple interest can be rearranged to find any of the variables when the values of the other three variables are known.

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Finding the interest rate, r To find the interest rate per annum, r, given the values of P, I and t: r = 100I Pt where P is the principal, I is the interest and t is the time in years. Refer to Example 8 page 530

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Finding the term, t. To find the number of years or term of an investment, t years, given the values of P, I and r: t = 100I Pr where P is the principal, I is the amount of interest and r is the rate per annum. Refer to Example 9 page 531

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Finding the principal, P. To find the value of the principal, P given the values of I, r and t: P = 100I rt To find the value of the principal, P given the values of A, r and t: P = A____ ( 1 + rt ) 100 Refer to Example 10 page 531

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How to use the graphics TI-Nspire CAS to solve simple interest problems. Refer to page 532 of your text book and follow the steps. Note: There are two methods to solve simple interest problems using the CAS calculator. Method 1: Form a table and Method 2: Draw a graph Work through the example on page 532 using your calculator to trial both methods.

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