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Financial Maths Chapter 16 16 A and B – purchasing goods (simple interest) and buying on terms
What is financial maths about? It looks at: Purchasing goods (eftpos, cash, credit, layby, loan, buying on terms) Investing/loans (how interest builds up) Interest (if you borrow money, usually you pay it back with interest, which is extra money you pay on top of the amount you initially borrowed) Value (profit and loss – depreciation) These are important, real life issues that we all have to understand and deal with especially when making big purchases like a car or home
Skills and knowledge What should you already know? Percentages (e.g. 75% is the same as 0.75) Substitution using a formula Calculator work (e.g. using fractions, multiplying by decimals) Multiplying (e.g. ab is a multiplied by b) General knowledge (e.g. how many weeks/months in a year) What will you learn? How to apply these skills to real life financial problems and scenarios What skills will you be demonstrating? Able to work with realistic information to work out loan repayments, interest payable and so on Able to apply formulas to real data Breaking down the question to work out what information you have, and how to apply this information to work out the required solution
Simple interest This is interest that is based on the initial amount you borrowed Simple interest formula: or Principle (P) = the initial amount you borrowed Rate (R) = the interest rate (as a percentage) Time (T) = how many years the loan is for The total amount you will pay back is: We pay interest when we borrow money or use the bank’s money e.g. credit card, loans, investments We earn interest when we invest money e.g. in a savings account
16A – Purchasing goods
16A – (continued)
Class work (finish for homework) Ex 16A p540 – 1, 2, 3, 4, 6 (complete 8 and 10 as extension work)
Buying on terms When buying an item on terms: 1. a deposit is paid 2. the balance is paid off over an agreed period of time with set repayments 3. the set repayments may be calculated as a stated arbitrary amount (same amount for each repayment), or by using an interest rate 4. total money paid will be higher than the initial cash price Example: buying furniture – pay a 10% deposit and pay off the rest in instalments over 3 years
16B – Buying on terms Worked example: when the repayment amount is known The cash price of a computer is $2400. It can also be purchased on the following terms: 25% deposit and payments of $16.73 per week for 3 years. Calculate the total cost of the computer. In order to calculate the total cost, we need to work out the deposit first: Deposit: 25% of 2400 = 2400 x 0.25 = 600 Initial deposit is $600 Now we need to work out the total amount of repayments: $16.73 per week for three years How many weeks in a year? 52 How many weeks in 3 years? 52 x 3 = 156 weeks Repayments are $16.73 per week for 156 weeks = 16.73 x 156 = 2609.88 Add in the initial deposit 2609.88 + 600 = 3209.88 Total cost of the computer is $3209.88 (final answer in dollars)
16B (continued) Worked example: when the interest rate is known A diamond engagement ring has a purchase price of $2500. Michael buys the ring on the following terms: 10% deposit with the balance plus simple interest paid monthly at 12% p.a. over 3 years. a) Calculate the amount of the deposit. Deposit = initial purchase price x deposit percentage = 2500 x.10 (10% can be written as 0.1) = 250 Initial deposit is $250 b) What is the balance owing after the initial deposit? Balance owing = initial amount – deposit = 2500 – 250 = 2250 Balance owing is $2250
A diamond engagement ring has a purchase price of $2500. Michael buys the ring on the following terms: 10% deposit with the balance plus simple interest paid monthly at 12% p.a. over 3 years. d) What is the total amount to be repaid? This is the balance owing plus the interest payable = 2250 + 810 = 3060 Total amount to be repaid is $3060 e) Find the amount of each monthly repayment. The ring is going to be repaid over 3 years, which is 36 months (3 x 12) Repayments = total amount to be repaid divided by number of months 3060 ÷ 36 = 85 The monthly repayments will be $85 per month
Class work Ex 16B page 543 questions 1, 2, 3ace, 6, 8, 10ace, 11
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