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Unit two | general mathematics

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1 Unit two | general mathematics
Financial arithmetic Unit two | general mathematics

2 Percentage change Calculating the Percentage Change
The percentage change is found by taking the change that has occurred and expressing it as a percentage of the starting value. Calculating the Percentage Change % π‘β„Žπ‘Žπ‘›π‘”π‘’= π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘β„Žπ‘Žπ‘›π‘”π‘’ π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’ Γ—100

3 Percentage change % π‘β„Žπ‘Žπ‘›π‘”π‘’= π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘β„Žπ‘Žπ‘›π‘”π‘’ π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’ Γ—100 eg1. A pair of shoes is marked down from $125 to $80. Find the percentage change of the shoes. % π‘β„Žπ‘Žπ‘›π‘”π‘’= π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘β„Žπ‘Žπ‘›π‘”π‘’ π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’ Γ—100 = Γ—100 =36 %

4 Percentage change % π‘β„Žπ‘Žπ‘›π‘”π‘’= π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘β„Žπ‘Žπ‘›π‘”π‘’ π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’ Γ—100 eg2. Petrol increases in price from $1.20 per litre to $1.35 per litre. Find the percentage change in the cost of petrol. % π‘β„Žπ‘Žπ‘›π‘”π‘’= π΄π‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘β„Žπ‘Žπ‘›π‘”π‘’ π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘ƒπ‘Ÿπ‘–π‘π‘’ Γ—100 = Γ—100 =12.5 %

5 Unit two | general mathematics
Now do Ex3.2 q1ac, 2, 9, 14, 15 Unit two | general mathematics

6 Finding the new cost of a marked up / down item
When an item is marked down (reduced in price) by a percentage, r, we can find the new price of the item using: When an item is marked up (increases in price) by a percentage, r, we can find the new price of the item using: 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100βˆ’π‘Ÿ) 100 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100+π‘Ÿ) 100

7 marked down (reduced) marked up (increased) eg
marked down (reduced) marked up (increased) eg. Reduce $240 by 25% 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100βˆ’π‘Ÿ) 100 =240Γ— (100βˆ’25) 100 =240Γ— = $180 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100βˆ’π‘Ÿ) 100 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100+π‘Ÿ) 100 eg. Increase $130 by 15% 𝑛𝑒𝑀 π‘π‘Ÿπ‘–π‘π‘’=π‘œπ‘™π‘‘ π‘π‘Ÿπ‘–π‘π‘’ Γ— (100+π‘Ÿ) 100 =130Γ— (100+15) 100 =130Γ— = $149.50

8 Unit two | general mathematics
Now do Ex3.2 Q3ac, 4ac, 5, 7, 13 Ex3.3 Q7 Unit two | general mathematics

9 Price changes using a spreadsheet

10 Unit two | general mathematics
Now do Ex3.3 Q22 Unit two | general mathematics

11 Shares and dividends When you buy shares in a company, you effectively own a portion of the company. If the company isn’t going well, the price you paid for your shares decreases in value. Likewise, when it’s successful, the value of your share increases in value. Any profit made is distributed to shareholders and paid as a dividend. 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘ƒπ‘’π‘Ÿ π‘†β„Žπ‘Žπ‘Ÿπ‘’= π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  eg. A company with shares makes an annual profit of $ , Calculate the dividend payable per share. 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ = =0.68 =68 cents per share

12 Shares and dividends 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘ƒπ‘’π‘Ÿ π‘†β„Žπ‘Žπ‘Ÿπ‘’= π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  eg2. A company declares a total dividend of $ and a dividend per share of 60 cents. How many shares are in the company? 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ = π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  Number of Shares = π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ = =

13 Percentage dividend Shares in different companies vary in price drastically from cents to hundreds of $$. When deciding to buy shares, investors often look at the company’s Percentage Dividend. This shows the investor what proportion of their investment comes back to them as a dividend. π‘ƒπ‘’π‘Ÿπ‘π‘’π‘›π‘‘π‘Žπ‘”π‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑= 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘π‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ Γ—100 eg. Calculate the percentage dividend on a share that cost $1.25 and paid a dividend of 8 cents per share. π‘ƒπ‘’π‘Ÿπ‘π‘’π‘›π‘‘π‘Žπ‘”π‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 = Γ—100 =6.4 %

14 Unit two | general mathematics
Now do Ex3.3 Q1,2,3 Unit two | general mathematics

15 Price-to-earnings ratio
The price-to-earnings ratio (P/E Ratio) is another way of comparing shares, by looking at the current share price and the annual dividend. The P/E Ratio gives us an indication of how much shares cost per dollar of profit. 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ = π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ eg. Calculate the price-to-earnings ratio for a company with a share price of $2.20 and gives a dividend of 10 cents. 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ= =22

16 Price-to-earnings ratio
𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ = π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ eg2. Calculate the price of a share if the price-to-earnings ratio is 15 and pays a dividend of 20 cents. 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ= π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’=𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ ×𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ =15Γ—0.20 =$3.00

17 Price-to-earnings ratio
𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ = π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ eg3. Calculate the dividend paid per share if the price-to-earnings ratio is 36 and the share price is $1.44 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ= π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’= π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ = =0.04 =4 𝑐𝑒𝑛𝑑𝑠

18 What is the dividend per share payable to shareholders?
𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ = π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘ƒπ‘’π‘Ÿ π‘†β„Žπ‘Žπ‘Ÿπ‘’= π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘†β„Žπ‘Žπ‘Ÿπ‘’π‘  eg4. A company that has shares declares an annual gross profit of $ They pay 20% of this in tax, and reinvests 30% of the remaining profit (net profit). What is the dividend per share payable to shareholders? What is the Price-to-earnings ratio if the current share price is $38.90 ? 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’= π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘ β„Žπ‘Žπ‘Ÿπ‘’π‘  π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 β†’ 20% paid in tax, 80% remaining after tax = Γ— =$6,720,208 30% of total after tax reinvested, leaving 70% dividend = Γ—0.70 =$4,407,145.60 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’= π‘‡π‘œπ‘‘π‘Žπ‘™ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘ β„Žπ‘Žπ‘Ÿπ‘’π‘  = =$5.88 𝑃/𝐸 π‘…π‘Žπ‘‘π‘–π‘œ= π‘†β„Žπ‘Žπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’ = =6.62

19 Unit two | general mathematics
Now do Ex3.3 Q5,6,11ac,13 Unit two | general mathematics

20 Calculating cost with & without G.S.T.
GST is a 10% Goods and Services Tax imposed on some products and services. We can use the following chart to calculate the price of goods with/without GST eg1. The price of a bottle of Juice is $4.20 before GST is added. Find the cost of the item if GST was added to this price. π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘€π‘–π‘‘β„Ž 𝐺𝑆𝑇= 4.20 Γ—1.1 =$4.62

21 Calculating cost with & without G.S.T.
eg2. The price of dress is $ before GST is added. Find the cost of the item if GST was added to this price. π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘€π‘–π‘‘β„Ž 𝐺𝑆𝑇=89.00 Γ—1.1 =$97.90

22 Calculating cost with & without G.S.T.
eg3. The price of corn flakes is $4.90 including GST. Find the price of the item before GST was added. π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘€π‘–π‘‘β„Žπ‘œπ‘’π‘‘ 𝐺𝑆𝑇= =$4.45

23 Calculating the G.S.T. To find the amount of GST on an item, decide whether the price already includes GST and choose the formula which applies. eg1. Calculate the GST on an item, if the price is $79.00 with GST included. eg2. Calculate the GST on an item, if the price is $53.40 before GST 𝐺𝑆𝑇=53.40 Γ—0.1 =$5.34 Γ— 0.1 Γ·11 𝐺𝑆𝑇= =$7.18

24 Unit two | general mathematics
Now do Ex3.3 Q17, 9, 10, 12, 20 Unit two | general mathematics

25 Simple interest 𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100
When you borrow money, you pay for the privilege of lending and spending someone else’s money by paying them interest. In the same way, when you invest money you can get interest paid on your money. Simple Interest is one type of interest, calculated using: π‘†π‘–π‘šπ‘π‘™π‘’ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘= π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ Γ—π‘…π‘Žπ‘‘π‘’ Γ—π‘‡π‘–π‘šπ‘’ 100 𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ βˆ’π‘‘β„Žπ‘’ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘šπ‘œπ‘›π‘’π‘¦ π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘’π‘‘ π‘œπ‘Ÿ π‘‘π‘’π‘π‘œπ‘ π‘–π‘‘π‘’π‘‘ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑑=π‘‘π‘–π‘šπ‘’ π‘‘β„Žπ‘Žπ‘‘ π‘‘β„Žπ‘’ π‘šπ‘œπ‘›π‘’π‘¦ 𝑖𝑠 π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘’π‘‘/𝑖𝑛𝑣𝑒𝑠𝑑𝑒𝑑 π‘“π‘œπ‘Ÿ (π‘¦π‘’π‘Žπ‘Ÿπ‘ )

26 π‘†π‘–π‘šπ‘π‘™π‘’ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘= π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ Γ—π‘…π‘Žπ‘‘π‘’ Γ—π‘‡π‘–π‘šπ‘’ 100
𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100 Eg1. Calculate the simple interest payable on a loan of $40 000, borrowed at a rate of 12% over 5 years. 𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 = Γ— 12 Γ— =$24 000 How much will the borrower owe to the bank in total? π‘‡π‘œπ‘‘π‘Žπ‘™ π‘ƒπ‘Žπ‘¦π‘Žπ‘π‘™π‘’=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™+πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = = $64 000

27 π‘†π‘–π‘šπ‘π‘™π‘’ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘= π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ Γ—π‘…π‘Žπ‘‘π‘’ Γ—π‘‡π‘–π‘šπ‘’ 100
𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100 Eg2. A term deposit of $30,000 attracts 4.5% interest over 6 years. How much interest is made? 𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 = Γ— 4.5 Γ— =$8 100

28 π‘†π‘–π‘šπ‘π‘™π‘’ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘= π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ Γ—π‘…π‘Žπ‘‘π‘’ Γ—π‘‡π‘–π‘šπ‘’ 100
𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100 Eg3. A $13,500 loan attracts an interest rate of 16% over 90 months. How much interest is paid on this loan? Convert 90 months into years: π‘šπ‘œπ‘›π‘‘β„Žπ‘  12 π‘šπ‘œπ‘›π‘‘β„Žπ‘  =7.5 π‘¦π‘’π‘Žπ‘Ÿπ‘  𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 = Γ— 16 Γ— =$16 200 What is the total amount payable on the loan? Total = Principal + Interest = = $29 700

29 𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 100 Eg4. A $ loan attracts an interest rate of 11% over 3 years and 3 months a) How much interest is paid on this loan? Convert 3 years and 3 months into years: 3 π‘¦π‘’π‘Žπ‘Ÿπ‘ + 3 π‘šπ‘œπ‘›π‘‘β„Žπ‘  12 π‘šπ‘œπ‘›π‘‘β„Žπ‘  =3.25 π‘¦π‘’π‘Žπ‘Ÿπ‘  𝐼= 𝑃 Γ— π‘Ÿ Γ— 𝑑 = Γ— 11 Γ— =$3 575 b) What is the total amount payable on the loan? Total = Principal + Interest = = $13 575 c) If making equal monthly repayments, how much would I be charged each month? Γ— = =$348.08

30 Unit two | general mathematics
Now do Ex3.4 Q1, 5, 6 Unit two | general mathematics

31 Simple interest We can rearrange the formula to solve other unknowns:

32 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃
Solving the Principal ($) Solving the Rate (%) Solving the Time (years) 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 eg1. Find the time period of a $2200 loan which produces interest of $440 at 8% interest per annum. 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 = 100 Γ— Γ—2200 = =2.5 π‘¦π‘’π‘Žπ‘Ÿπ‘  𝑑=? 𝐼=$440 π‘Ÿ=8% 𝑃=$2200

33 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑
Solving the Principal ($) Solving the Rate (%) Solving the Time (years) 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 eg2. Find the rate of an $8000 loan which produces interest of $1750 over 5 years π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 = 100 Γ— Γ— 5 = =4.375 % π‘Ÿ=? 𝐼=$1750 𝑑=5 𝑃=$8000

34 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑
Solving the Principal ($) Solving the Rate (%) Solving the Time (years) 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 𝑑= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑃 π‘Ÿ= 100 Γ— 𝐼 𝑃 Γ— 𝑑 eg3. Find the principal of a loan that attracts $ interest over 3.5 years at a rate of 13.25% per annum 𝑃= 100 Γ— 𝐼 π‘Ÿ Γ— 𝑑 = 100 Γ— Γ— 3.5 = = $2000 π‘Ÿ=? 𝐼=$1750 𝑑=5 𝑃=$8000

35 Unit two | general mathematics
Now do Ex3.4 Q3, 4, 16, 18, 22, 13 Unit two | general mathematics

36 CASh flow - Simple interest non-annual interest calculations
Interest rates are usually advertised at a per annum rate, however in reality interest is usually accrued more frequently than this – Quarterly, Monthly, Weekly, Daily etc. eg1. How much interest is paid on a monthly balance of $900 with a simple interest rate of 11% per annum? 𝐼= π‘ƒπ‘Ÿπ‘‘ 100 𝐼= 900Γ—11Γ— 𝐼=$8.25 P=900 r=11 t= 1 12

37 CASh flow - Simple interest non-annual interest calculations
eg2. How much interest is paid on a weekly balance of $1400 with a simple interest rate of 8.2% per annum? 𝐼= π‘ƒπ‘Ÿπ‘‘ 100 𝐼= 1400 Γ— 8.2 Γ— 𝐼=$2.21 P=1400 r=8.2 t= 1 52

38 CASh flow - Simple interest non-annual interest calculations
eg3. How much interest is paid on a quarterly balance of $3200 with a simple interest rate of 6.8% per annum? 𝐼= π‘ƒπ‘Ÿπ‘‘ 100 𝐼= 3200 Γ— 6.8 Γ— 𝐼=$54.40 P=3200 r=6.8 t= 1 4

39 CASh flow - Simple interest minimum balance calculations
When applying interest to an account, it is common practice to apply interest to the minimum balance during a set time period. In investment accounts, the bank finds the lowest amount of money that you have in the account during that time and applies interest to that amount. eg1. How much interest is paid on this account if interest paid monthly at 3% per annum and the opening balance is $1500 ? $1500 βˆ’ $150 = $1350 $ $220 = $1570 Minimum Balance $1570 βˆ’ $500 = $1070 $ $120 = $1470

40 CASh flow - Simple interest minimum balance calculations
Eg1 (continued). How much interest is paid on this account if interest paid monthly at 3% per annum and the opening balance is $1500 ? $1500 βˆ’ $150 = $1350 $ $220 = $1570 Minimum Balance $1570 βˆ’ $500 = $1070 $ $120 = $1470 𝐼= π‘ƒπ‘Ÿπ‘‘ 100 𝐼= Γ— 3 Γ— 𝐼=$2.68 P=1070 r=3 t= 1 12

41 Unit two | general mathematics
Now do Ex3.4 Q7ab,8,9,14 Unit two | general mathematics

42 compound interest With simple interest, the interest paid is constant and spread out over a loan period. Compound Interest is different as interest is calculated and added periodically throughout the loan. This means that the dollar amount of interest paid changes in each period based on the balance of the loan for that period.

43 compound interest – paid annually
Calculating Compound Interest with interest paid annually: 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ βˆ’π‘‘β„Žπ‘’ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘šπ‘œπ‘›π‘’π‘¦ π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘’π‘‘ π‘œπ‘Ÿ π‘‘π‘’π‘π‘œπ‘ π‘–π‘‘π‘’π‘‘ π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™π‘™π‘¦ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  𝑖𝑛 π‘‘π‘–π‘šπ‘’ π‘π‘’π‘Ÿπ‘–π‘œπ‘‘

44 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 =5,000 (1+ 4 100 ) 1
𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  COMPOUND INTEREST 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 eg1. If I invest $5000 in a compound deposit at 4% interest per annum paid annually: a) How much do I have after one year? 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 After FIRST year 𝑃=$5,000 π‘Ÿ=4% 𝑛=1 =5,000 ( ) 1 =5,000 (1.04 ) 1 =$5,200

45 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 =5,000 (1+ 4 100 ) 5
𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  COMPOUND INTEREST 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 eg1. If I invest $5000 in a compound deposit at 4% interest per annum paid annually: b) How much do I have after 5 years? 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 After 5 years 𝑃=$5,000 π‘Ÿ=4% 𝑛=5 =5,000 ( ) 5 =5,000 (1.04 ) 5 =$6,083.26 How much Interest has been earned? 𝐼=π΄βˆ’π‘ƒ= βˆ’5000=$

46 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 =8,000 (1+ 5 100 ) 2
𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  COMPOUND INTEREST 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 eg2. If I invest $8000 in a compound deposit at 5% interest per annum paid annually: a) How much do I have after 2 years? 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 After 2 years 𝑃=$8,000 π‘Ÿ=5% 𝑛=2 =8,000 ( ) 2 =8,000 (1.05 ) 2 =$8,820

47 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 =8,000 (1+ 5 100 ) 5
𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  COMPOUND INTEREST 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 eg2. If I invest $8000 in a compound deposit at 5% interest per annum paid annually: b) How much do I have after 5 years? 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 After 5 years 𝑃=$8,000 π‘Ÿ=5% 𝑛=5 =8,000 ( ) 5 =8,000 (1.05 ) 5 =$10,210.25

48 compound interest 𝑃= 𝐴 (1+ π‘Ÿ 100 ) 𝑛 π‘Ÿ=100 (( 𝐴 𝑃 ) 1 𝑛 βˆ’1)
𝑃= 𝐴 (1+ π‘Ÿ 100 ) 𝑛 Finding the Principal: π‘Ÿ=100 (( 𝐴 𝑃 ) 1 𝑛 βˆ’1) Finding the Rate: 𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ βˆ’π‘‘β„Žπ‘’ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘šπ‘œπ‘›π‘’π‘¦ π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘’π‘‘ π‘œπ‘Ÿ π‘‘π‘’π‘π‘œπ‘ π‘–π‘‘π‘’π‘‘ π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™π‘™π‘¦ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  𝑖𝑛 π‘‘π‘–π‘šπ‘’ π‘π‘’π‘Ÿπ‘–π‘œπ‘‘

49 𝑃= 𝐴 (1+ π‘Ÿ 100 ) 𝑛 π‘Ÿ=100 (( 𝐴 𝑃 ) 1 𝑛 βˆ’1) eg1. A car loan with a rate of 8.9% p.a. over 5 years, has a final value of $62,423. What was the purchase price of the car? b) Another loan option attracted $18,000 interest over 4 years, compounding annually. What rate was this option? 𝑃= 𝐴 (1+ π‘Ÿ 100 ) 𝑛 = ( ) 5 =$40,757.28 π‘Ÿ=8.9 𝐴=62423 𝑛=5 π‘Ÿ= ? 𝑃= 𝐴= = 𝑛=4 π‘Ÿ=100( ) βˆ’1 = 9.58%

50 Unit two | general mathematics
Now do Ex3.5 Q2,4,1,3,5,6 Unit two | general mathematics

51 compound interest – non-annual
Calculating Compound Interest with interest paid non-annually: 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 𝐴=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ 𝑝𝑙𝑒𝑠 π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ 𝑃=π‘ƒπ‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ βˆ’π‘‘β„Žπ‘’ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ π‘œπ‘“ π‘šπ‘œπ‘›π‘’π‘¦ π‘π‘œπ‘Ÿπ‘Ÿπ‘œπ‘€π‘’π‘‘ π‘œπ‘Ÿ π‘‘π‘’π‘π‘œπ‘ π‘–π‘‘π‘’π‘‘ π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™π‘™π‘¦ π‘Ÿ=πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ π‘π‘’π‘Ÿ π‘Žπ‘›π‘›π‘’π‘š (%) 𝑛=π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘›π‘‘π‘–π‘›π‘”π‘  𝑖𝑛 π‘‘π‘–π‘šπ‘’ π‘π‘’π‘Ÿπ‘–π‘œπ‘‘

52 compound interest – non-annual
𝐴=𝑃 (1+ π‘Ÿ 400 ) 𝑛 Compounding Quarterly: Compounding Monthly: Compounding Weekly: Compounding Fortnightly: Compounding Daily: 𝐴=𝑃 (1+ π‘Ÿ ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ ) 𝑛 𝐴=𝑃 (1+ π‘Ÿ ) 𝑛

53 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛
𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 Eg1. Calculate the final balance for a $3000 investment at 4% pa for 5 years, compounding weekly 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 = =$ A = ? P = 3000 r = 4 n = (5 x 52) = 260 Compoundings /yr = 52 What if it was compounding daily? 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 = =$

54 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛
𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 Eg2. Calculate the Interest on a $20000 loan at 12% per annum for 4 years, compounding a) Monthly b) Quarterly c) Fortnightly MONTHLY 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 = =$ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = 𝐴 βˆ’ 𝑃 = βˆ’20 000 =$ A = ? P = 20000 r = 12 n = (4 x 12) = 48 Compoundings /yr = 12

55 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛
𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 Eg2. Calculate the Interest on a $20000 loan at 12% per annum for 4 years, compounding a) Monthly b) Quarterly c) Fortnightly QUARTERLY 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 = =$ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = 𝐴 βˆ’ 𝑃 = βˆ’20 000 =$ A = ? P = 20000 r = 12 n = (4 x 4) = 16 Compoundings /yr = 4

56 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛
𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 Eg2. Calculate the Interest on a $20000 loan at 12% per annum for 4 years, compounding a) Monthly b) Quarterly c) Fortnightly FORTNIGHTLY 𝐴=𝑃 (1+ π‘Ÿ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘šπ‘π‘œπ‘’π‘‘π‘–π‘›π‘”π‘  π‘π‘’π‘Ÿ π‘¦π‘’π‘Žπ‘ŸΓ—100 ) 𝑛 = =$ πΌπ‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = 𝐴 βˆ’ 𝑃 = βˆ’20 000 =$ A = ? P = 20000 r = 12 n = (4 x 26) = 104 Compoundings /yr = 26

57 Unit two | general mathematics
Now do Ex3.5 Q8,11,12,16 Unit two | general mathematics

58 Applications of compound interest – inflation
Inflation is a term used to describe a general increase in prices over time. In reality, when analyzing profits and losses over a period of time, we must take inflation into consideration. Inflation can be measured by the inflation rate, which is an annual percentage change of the CPI (Consumer Price Index) For example – A house costs $ and sells for $ years later. Considering prices usually increase over time, has a profit really been made? Or has the price just increased as per the rate of inflation for that time period?

59 Applications of compound interest – inflation
Eg. An investment property is purchased for $ and is sold 4 years later for $ If the annual average inflation is 1.7% per annum, has this been a profitable investment? Inflation is an application of compound interest – find the value of $250,000, 4 years on…… 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 = = (1.017) 4 =$ Inflated amount = $ Sell Price = $ They have made a real profit of $ 𝑷=πŸπŸ“πŸŽ 𝟎𝟎𝟎 𝒓=𝟏.πŸ• 𝒏=πŸ’ 𝑨= ?

60 Applications of compound interest – inflation
Eg2. An business is purchased for $ and is sold 3 years later for $ If the annual average inflation is 2.1% per annum, has a real profit been made? Inflation is an application of compound interest – find the value of $120000, 3 years on…… 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 = = (1.021) 3 =$ Inflated amount = $ Sell Price = $ They have not made a real profit. 𝑷=𝟏𝟐𝟎 𝟎𝟎𝟎 𝒓=𝟐.𝟏 𝒏=πŸ‘ 𝑨= ?

61 Applications of compound interest – inflation
Eg3. A person invests $2000 wanting to purchase a $2500 item in 3 years. They reach this goal by investing in an account paying compound interest quarterly. What rate is the investment paying? The item increases with inflation at a rate of 1.9% pa. How much does the item actually cost at the end of the 3 years? How much should they have invested to buy the item at the inflated price? a) 𝑷=𝟐𝟎𝟎𝟎 𝒓= ? 𝒏=πŸ‘ Γ—πŸ’ 𝑨=πŸπŸ“πŸŽπŸŽ

62 Applications of compound interest – inflation
Eg3. A person invests $2000 wanting to purchase a $2500 item in 3 years. b) The item increases with inflation at a rate of 1.9% pa. How much does the item actually cost at the end of the 3 years? 𝐴=𝑃 (1+ π‘Ÿ 100 ) 𝑛 = = =$ 𝑷=πŸπŸ“πŸŽπŸŽ 𝒓=𝟏.πŸ— 𝒏=πŸ‘ 𝑨= ? c) How much should they have invested to buy the item at the inflated price?

63 Applications of compound interest – inflation
Eg3. A person invests $2000 wanting to purchase a $2500 item in 3 years. c) How much should they have invested to buy the item at the inflated price? 𝐴=𝑃 (1+ π‘Ÿ 400 ) 𝑛 𝑃= 𝐴 (1+ π‘Ÿ 400 ) 𝑛 𝑷=? 𝒓=πŸ•.πŸ“πŸ 𝒏=πŸ‘ Γ—πŸ’ 𝑨=πŸπŸ”πŸ’πŸ“.𝟐𝟐 𝑃= ( ) 12 =$

64 Unit two | general mathematics
Now do Ex3.5 Q9,10,15,17 Unit two | general mathematics

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