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Percentage change

Percentage change. Discount:. Example: a How much is saved if a 25% discount is offered on an item marked $8.00? Discount = 25×8 = 200 = $2 100 100 b What is the new discounted price of this item? New price = original price - discount = 8 - 2 =$6 or

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Percentage change

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  1. Percentage change Discount: Example: a How much is saved if a 25% discount is offered on an item marked $8.00? Discount = 25×8 = 200 = $2 100 100 bWhat is the new discounted price of this item? New price = original price - discount = 8 - 2 =$6 or New price = (100 - r)× original price = 75×8 = $6 100 100

  2. Increase: Example: aIf petrol prices increase by 10%, what is the amount of the increase when the price is 99.0 cents per litre? Increase = 10 × 99 = 9.9 cents 100 bWhat is the new price per litre for petrol? New price = 99 + 9.9 = 108.9 cents per litre Given the original price and the new price of an item, we can work out the percentage change.

  3. Example: aIf the price of a book is reduced from $25 to $20, what percentage discount has beenapplied? percentage discount = discount × 100 = 5 × 100 =20 % original price 25 bIf the price of a book is increased from $20 to $25, what percentage increase has been applied? percentage increse = increase × 100 = 5 × 100 =25 % original price 20 Sometimes we are given the new price and the percentage increase or decrease (r%), and askedto determine the original price. We can do this by usingthe above formulas for new price and rearange them to find the original price . Example:Suppose that Steve has a $60 gift voucher from his favourite shop. aIf the store has a ‘25% off’ sale, what is the original value of the goods he can now buy? New price = original price ×100 - r 100 60 = original price × 75 100 original price = 100 ×60 = $80 75

  4. bIf the store raises its prices by 25%, what is the original value of the goods he can now buy? new price = original price × 100 +r 100 60 = original price × 125 100 original price = 100 × 60 = $48 125 Simple interest The price of borrowing or lending money is calledinterest. Thesimple interest is the interest that is calculated only by the initial amount of investment or loan and is not calculated according to the balance.The following formula is used for simple interest: From the graph we can see that the relationship of ‘time’ and ‘simple interest’ is linear. The slope or gradient of a line whichcould be drawn through these points is numericaly equal to the interest rate.

  5. To determine the amount of the investment, the interest earned is added to the amountinitially invested. Example:How much interest would be due on a loan of $5000 at 10% per annum for six months? I = Prt = 5000 × 10 × 0.5 = 2000 = $250 100 100 100 Example:Find the total amount owed on a loan of $10 000 at 12% per annum simple interest at the endof two years. I = Prt = 10000 × 12 × 2 = 240000 = $2400 100 100 100 A = P+I =10 000 + 2400 = $12 400

  6. Using the simple interest formula we can find the Principal, the Interest Rate and the Period. Example: Find the length of time it would take for $50 000 invested at an interest rate of 8% per annumto earn $10 000 interest. I = Prt 100 t = 100 I = 100× 10 000 = 25 years Pr 50 000 × 8 Example: Find the amount that should be invested in order to earn $1350 interest over 3 years at aninterest rate of 4.5% per annum. I = Prt 100 P = 100 I = 100 × 1350 = $10 000 rt 4.5 × 3 Example: Find the rate of simple interest charged per annum if a loan of $20 000 incurs interest of$12 000 after eight years. I = Prt 100 r = 100 I = 100 × 12 000 = 7.5% per annum Pt 20 000 × 8

  7. Compound interest Compound interest is different from simple interest because is calculated according to the new balance and not according to the initial amount.The relationship of the ‘compount interest’ against ‘time’ is not linear and is clearly shown on the graph below: Tofind the compount interestwe can use the ‘Compount Interest Formula’ or the ‘TVM’ solver which is on the calculator menu of your CAS.

  8. To find the amount of interest earned, we need to subtract the initial investment (P) from the final amount(A).I = A - P Example: aDetermine the amount of money accumulated after four years if $10000 is invested at aninterest rate of 9% per annum, compounded annually, giving your answer to the nearestdollar. Using the formula: A = P (1+ r/n )t 100 A = 10000 ( 1 + 9/100)4 =10000×1.4116 =$14116 to the nearest dollar Using the TVM The interpretation of each function of ‘finance solver is as follows: N = number of periods I% = interest PV=initial amount (invested or borrowed) PMT= repayments (not applicable) FV = final amount PpY = payments in a year CpY = the times that the interest is compounded in a year Note:We enter +when we receive money (loans) and - when we give money (repayments,investements)

  9. bDetermine the amount of interest earned. I = A - P I = 14116 - 10000 = $ 4116 Example: aDetermine the amount accrued if $2700 is invested at an interest rate of 6% per annum for aperiod of two years and interest is compounded monthly. Using the formula: A = P (1+ r/n )nt 100 A = 2700 ( 1 + 6/12)12×2 = $3043.33 100 Example: How much money must you deposit at 7% per annum compound interest, compounding yearly,if you require $10 000 in three years’ time? Give your answer to the nearest dollar. Using the finance solver

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