HSC SC H HEAD ST START L T LECTU TURE Standard rd M Mathematics th October 2 Satu turday 5 5 th 2019 Presented by: KRYSTELLE VELLA
First o of a all… WEL WELCO COME E TO Y YOUR HSC Y YEAR!
By the end of today’s lecture… You will: learn stu techniques to prepare yourself for a tudy t successful year ahead learn the first few topics of Standard Maths! q Financial M Maths q Measureme ment q Ne Netw twor orks ks tions about anything you are unsure of! ask q questi
STUDY T TECHNI NIQUES
How to study for Standard Maths Although you don’t have exams for a while, it is a great i idea to learn s study t techniques f for S Standard M Maths n now ! q Start the year with a fr fresh b book, , and keep it up-to-date and neat throughout. q If a concept confuses you now, seek extra h help before the year goes on (i.e. asking for extra help, YouTube videos etc!) q Get into the habit of showing all y your w working. . q As you learn new formulas, create flashcards to help you practice and learn t them o off b f by hea heart. q Begin thinking about your exam technique to today.
Topic 1 1: Financial M Mathematics
In Year 11, you would have learned how to: ü calculate simple i interest (I= Prn ) ü calculate pe perce centag age in increa eases es and de decr creases ü use the straight-line method of de depr preci ciat ation ü calculate rates of pa pay (salaries, wages, overtime, commission etc!) ü calculate income t tax (PAYG) ü use bud budgets ts and calculate household e expenses Sound f fami miliar??
Now in Year 12: The two B topics we cover include: BROAD t 1. 1. Investments a and L Loans 2. 2. An Annuities
1. INVESTMENTS & LOANS Investments are used to GR GROW money. Future v value o of l loans When calculating the future value of loans, compound i interest is calculated on the initial amount borrowed/invested plus any interest charged or earned. To calculate the future value of a loan: 𝐺𝑊 = 𝑄𝑊 (1 + 𝑠) * wh where: FV FV - future value of the investment (final balance) • PV PV - present value of the principal (initial quantity of money) • • r r - rate of interest per compounding time period ( note: : this is expressed as a decimal) n - number of compounding time periods •
FUTURE VALUE OF LOANS Example q question: Brendan invests $14,000 over 6 years compounding annually. What is the future v value of the investment if the compound interest rate is 5% p.a.? So Solution: Remember t the f figures r required t to f fulfil t the f future v value f formula! • Present Value (PV) = $14 000 • Rate (r) = 5% p.a. (0.05) • Number of periods (n) = 6 ∴ 𝐺𝑊 = $14 000 (1 + 0.05) E 𝑮𝑾 = $𝟐𝟗 𝟖𝟕𝟐. 𝟒𝟓 (𝑢𝑝 2 𝑒𝑓𝑑𝑗𝑛𝑏𝑚 𝑞𝑚𝑏𝑑𝑓𝑡)
FUTURE VALUE OF LOANS When solving future v value q questions, , it is so important that you correctly find the value of the RA RATE and NO. O . OF P PERIO IODS! For e example: Jocelyn invests $5000 over 2 years compounding quarterly. Calculate the future value of the investment if the compound interest rate is 6% p.a.? How m many compounding p periods are th there? Wh What i t is th the interest r t rate per c compounding p period? 𝐺𝑊 = $5632.46
PRESENT VALUE OF LOANS We can also use the future-value formula to find the pr present va value of of an an in inves estmen ent. To To find p present v value: : 𝑮𝑾 𝑸𝑾 = (𝟐 + 𝒔) 𝒐
PRESENT VALUE OF LOANS Example q question: Calculate the present v value of an investment that has a future value of $25 000 after 8 years and earns 9.6% compound interest, compounding bi-annually. So Solution: Let’s break down the question to obtain our required values be befor ore we we insert them into the formula. • Future Value (FV) = $25 000 • Rate (r) = 9.6% p.a. compounding bi bi-an annual nually Ø = 4.8% (0.048) per compounding period • Number of periods (n) = 8 years compounding bi bi-an annual nually Ø = 16 compounding periods
PRESENT VALUE OF LOANS Solution co continued.. .. Therefore, the present value of this loan is equal to: 25 000 𝑄𝑊 = (1 + 0.048) LE 𝑸𝑾 = $𝟐𝟐 𝟗𝟏𝟖. 𝟔𝟓
FINDING THE INTEREST EARNED NOTE! Some questions may ask you to find t the i interest e earned only. In this case, we use the formula: 𝑱 = 𝑮𝑾 − 𝑸𝑾 Simply meaning that the interest earned is equal to the future value of the investment mi minus the present value (principal) of the investment. Careful not to confuse this with finding the interest ra rate .
FINDING THE INTEREST RATE To try and trick students, NESA may ask you to find the interest r rate used to calculate the present or future value of an investment. In these questions, we simply rearrange t the f future v value f formula. Ex Example le qu question: The present value of Henry’s investment is $31 250. After 4 years, this has grown to $35 000. If interest compounds annually, calculate the compound interest rate at which Henry’s investment is growing, correct to two decimal places.
FINDING THE INTEREST RATE Solution: So To begin, let’s insert the values we know into the future value formula. 𝑮𝑾 = 𝑸𝑾(𝟐 + 𝒔) 𝒐 In H Henry’s ’s i investment: Future Value (FV) = $35 000 • • Present Value (PV) = $31 250 Number of periods (n) = 4 • Rate (r) = ?? • 𝟒𝟔 𝟏𝟏𝟏 = 𝟒𝟐 𝟑𝟔𝟏(𝟐 + 𝒔) 𝟓 Now, we must use our algebraic knowledge to find the value of r.
FINDING THE INTEREST RATE Solution: So 35 000 31 250 = 31 250 31 250 (1 + 𝑠) S 1. 1. Remove the $31 250 from both sides by division. 1.12 = (1 + 𝑠) S Simplify. 2. T 1.12 = T (1 + 𝑠) S 3. 3. “Fourth-root” both sides to eliminate the 4. 1.028737345 = 1 + 𝑠 4. Simplify. Subtract 1 from either side, leaving the 𝑠 = 0.028737345 × 100% 5. 5. r on its own. Multiply by 100% to get a percentage answer. 𝒔 = 𝟑. 𝟗𝟖%
SOLUTIONS (previous slide)
FINDING THE INTEREST RATE Therefore, Henry’s investment grows at a compound interest rate of 2.87% p.a. (to two decimal places). How c can w we t test o t our a answer t to m make s sure i it’s t’s r right? t?
APPRECIATION Appreciation is the increase i in v value of goods. Ex Example le qu question: : Flynn bought a block of land in 2014 for $319,000. If the land appreciates at 5% p.a., calculate it’s value after 5 years. Answer to the nearest dollar. Solution: So 𝐺𝑊 = 𝑄𝑊(1 + 𝑠) * 𝐺𝑊 = 319 000 (1 + 0.05) m 𝐺𝑊 = $407 134 𝑼𝒊𝒇 𝒘𝒃𝒎𝒗𝒇 𝒑𝒈 𝒖𝒊𝒇 𝒎𝒃𝒐𝒆 𝐛𝐠𝐮𝐟𝐬 𝟔 𝐳𝐟𝐛𝐬𝐭 𝐣𝐭 $𝟓𝟏𝟖 𝟐𝟒𝟓, 𝒖𝒑 𝒖𝒊𝒇 𝒐𝒇𝒃𝒔𝒇𝒕𝒖 𝒆𝒑𝒎𝒎𝒃𝒔.
INFLATION Inflation is a steady in increa ease e in in the p price o of g goods a and s services in an economy over t time. Example q question: : In 2010, the average cost of 1L of Inflation affects both milk was $1.05. Accounting for the cost of living and the wages earned by an inflation rate of 6% p.a., individuals. determine the cost of 1L of milk in 2020. Wh Which f formula d do w we u use t to c calculate inflati tion?
INFLATION Let’s use the co compo pound d interest f formula. 𝐺𝑊 = 𝑄𝑊(1 + 𝑠) * 𝐺𝑊 = 1.05 (1 + 0.06) Ln 𝐺𝑊 = $1.88 Therefore, the cost of 1L of milk in 2020 is $ $1.8 .88 .
QUESTION TIME!! Question 1 10 ( (Multiple C Choice)– 2017 H HSC E Exam:
QUESTION TIME!! Question 1 17 ( (Multiple C Choice)– 2015 H HSC E Exam:
QUESTION TIME!! Question 2 26 ( (d) – 2015 H HSC E Exam: $369.17
DEPRECIATION To calculate depreciation, we use the de decl clining-balance m method fo formula: 𝑻 = 𝑾 𝟏 (𝟐 − 𝒔) 𝒐 wh where: S is the salvage value of the asset after n periods • • V 0 is the initial value of the asset r is the depreciation rate per period • • n is the number of period This f formula i is a an a application o of t the c compound i interest f formula!
DEPRECIATION Example q question: : Rodney purchased a Hyundai i30 in 2014 for $19 000. The car depreciates at 16% per annum. Calculate t the v value o of t the a asset a after 1 10 y years, c , correct t to t the n nearest do dollar ar. So Solution: n (1 − 𝑠) * 𝑇 = 𝑊 𝑇 = 19 000(1 − 0.16) Ln 𝑇𝑏𝑚𝑤𝑏𝑓 𝑤𝑏𝑚𝑣𝑓 = $𝟒𝟒𝟑𝟒 After 10 years, Rodney’s Hyundai is worth $3323, to the nearest dollar.
SHARES AND DIVIDENDS A share is when an individual/company owns p part o of a another company. . Shares are bought and sold on the stock market, including the ASX (Australian Securities Exchange). To buy a and s sell s shares, , we use a broker. . A broker receives a a brokerage f fee for their work – a percentage of the transaction.
Recommend
More recommend
