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Percents, Discounts and Interest PERCENTS: A percent is a representation of a number, compared to a total value of 100. A percent which is less than a whole, will be expressed as a number less than 100, while a number which is greater than one whole will be above 100. To calculate a percent… - from a fraction: - divide the numerator by the denominator, and multiply by 100 (eg. ¼ = 1 divided by 4, which is 0.25, multiply by 100 and the percent is 25%) - from a decimal: - multiply by 100 (o.58 x 100 = 58%)

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Percents, Discounts and Interest PERCENT INCREASE OR DECREASE: To calculate how much a number has increased or decreased, as a percent… - subtract to find the difference between the new number and the starting value ($15 new price, $20 starting price = decrease of $5) - express the difference as a fraction of the original value eg. 5 20 - set the fraction equal to a fraction out of 100 (proportion) eg. 5 = ___ 20 100 and then cross multiply… 5 x 100 divided by 20 = 25 (or 25%)

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Percents, Discounts and Interest DISCOUNTS: To calculate a discount, we need to find the percent of a number. To find the percent of a number… - multiply the number times the percent, expressed as a decimal (eg. 40% of 120 is 120 x 0.4 = 48) To find a discount, you simply do the above for the discount given. eg. A car with a value of $18 000 is discounted by 30%. What is the value of the discount? 18 000 x 0.3 = 5400 The value of the discount is $5 400.

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Percents, Discounts and Interest DISCOUNTS: To find the discounted price or value… - subtract the amount of the discount from the original value 18 000 – 5 400 = 12 600 The discounted price of the car is $12 600. You can also find the discounted price in one step… If 30% of the price has been removed, how much of the price is left? (100 – 30 = 70) 70% 18 000 x 0.7 = 12 600

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Percents, Discounts and Interest TAXES: If you must calculate the actual value you would pay for an item, you must include tax. Tax in Ontario right now on nearly all items is 13%, which is called the HST (Harmonized Sales Tax). If the discounted price of the car is $12 600, you would have to pay this cost, plus tax to actually purchase the car. To find the price with tax… - find 13% of the item, and add it to the cost 12 600 x 0.13 = 1638 + 12 600 = $14 238 OR… - find 113% of the item, because the total cost includes the price of the item (100%) and 13% tax 12 600 x 1.13 = $14 238 The cost of the car with tax is $14 238.

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Percents, Discounts and Interest INTEREST: Interest is the amount that is added to a value (usually money) when it is deposited or borrowed. Interest is given by banks to customers in return for keeping your money with them, which they can invest for additional profits. Interest is taken by banks and other lenders when money is borrowed by a customer for a period of time. Interest is calculated using a simple formula: I = Prt(“I” represents interest, “P” represents the principle, or the amount deposited or borrowed, “r” represents the rate of interest (as a decimal), and “t” represents the time in years)

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Percents, Discounts and Interest INTEREST: To calculate the interest on a particular amount deposited or borrowed… - substitute the value for each part of the formula into the equation: Eric borrowed $2 000 from the bank to go on a vacation. The bank loaned him the money, which must be repayed monthly over two years, with an interest rate of 8%. a) How much interest will Eric pay on his loan? b) What is the total amount Eric will need to pay the bank? c) How much will Eric’s monthly payments be?

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Percents, Discounts and Interest INTEREST: a)To calculate Eric’s interest… I = Prt I = 2000 x 0.08 x 2 I = 320 Eric will need to pay $320 in interest. b) To calculate Eric’s total amount to be re-payed… 2000 + 320 (Interest) = 2 320 Eric will need to pay $2 320 to the bank c) To calculate Eric’s monthly payment… 2 320 divided by 24 payments (monthly for 2 years) = 96.67 Eric will need to make monthly payments of $96.67.

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