MATHEMATICS

Grade 9

NUMBERS

Module 5

MONEY MATTERS

Money matters

CLASS WORK

1 Someone who starts a business, does it so that he can earn money for buying food, paying his water and power accounts, and paying for his other needs. Making money out of a business means that you have to get more money in from the business than you pay out to keep the business running. So, he makes a profit when his income is bigger than his expenses. If the expenses are more than the income, then he shows a loss. Another way of putting it is to look at gross income and net income. Gross income is the same as income above, namely all the money the business receives. Net income is what is left after you have subtracted expenses from the income. When income is more than expenses, net income is positive (a profit), but when income is less than expenses, net income is negative – i.e. a loss.

1.1 Calculate the profit or loss of the following businesses:

1.1.1 Income: R 36 000, R1 250 and R9 500; Expenses: R49 000

1.1.2 Expenses: R120 560; R15 030 and R55 250; Expenses: R85 000; R95 000 and R63 550

1.1.3 Patsy sells dried fruit and sweets from her stall in a large shopping centre. In March she paid R150 for the stall and R850 for the floor area in the centre. She sold dried fruit to the value of R1 500. In March she paid R250 to an assistant who relieves her two afternoons. She also made R2 840 on the sweets she sold in March. In April her expenses for renting the stall stayed the same, but she had to pay R50 more for the floor space. Her purchases of dried fruit and sweets during March and April cost her a total of R5 500. Her assistant earned R280 in April. Patsy’s phone account came to R860 for March and April. In April she sold dried fruit to the value of R1 370 and sweets for R2 550. Her packaging material for the two months came to R420. Did Patsy show a profit, or a loss for these two months? Show your calculations neatly.

2 All families have certain expenses that have to be paid. To do this, there must be an income – someone has to have a profitable business, or a job for which he or she receives a wage or a salary. To ensure that the important expenses are covered, most families budget. It is very easy. At the start of the month, you write down all the expected expenses for that month in order of importance. If all the critical expenses are less than the expected income for the month, then you have to decide what could be done with the rest: will a part of it be saved, or will all of it be spent? In this way you can avoid spending all your money on movies and parties, leaving nothing for the phone account! For example, the Jacobs family are expecting the following monthly expenses: R160 for municipal services, R240 for the telephone, R2 800 for groceries, R1 300 for a bond payment, R650 for the hire purchase payment on their car, R250 pocket money for the children, R150 school fees, R340 for petrol and R200 to save for a holiday. Mr and Mrs Jacobs together earn R8 200 per month.

2.1 Make budgets for Anna, Louise and Maggie. They are in grade 9, and each receives pocket money every month: Anna gets R450, Louise gets R220 and Maggie gets R600. Out of this they have to pay for clothes, make–up, entertainment, sweets and cell phone charges. Work in groups of three – each one takes one of the girls and makes her budget. You have to decide what the budget will be like. When everyone has finished, all the learners who worked out Anna’s budget get together and form groups of 3, 4, 5 or 6. Do the same for Louise and Maggie. Compare your budgets and set up a new, better budget in each group. Hand in your answer.

3 Someone who needs more money than he has in the bank may decide to borrow the money from someone, or from a bank. He pays the person who gives him the loan (we call this payment interest) and this payment depends on many factors, like the size of the loan. The interest rate also depends on many things. The loan amount plus the interest is paid together either at the end of the loan period or in regular repayments. If Mr Botha borrows R8 500 for six months at an annual (yearly) interest rate of 15%, then after six months he has to pay back the R8 500 plus the interest which comes to R637,50 for six months. (For a year it would be 15% of R8 500.) He repays R9137,50.

3.1 Mrs Petersen bakes cakes for three shops. She needs a new oven. She has some money saved, and intends to borrow the other R3 500 she needs from a bank. She borrows the money at an interest rate of 13,5% per annum. What is the amount she’ll have to pay the bank at the end of the year?

4 People often budget money to be saved. This is a good way to get money together for future large expenditures. One can save for a holiday, to paint the house, to buy a new car and (very important) for retirement when there might not be a regular income anymore. The money is saved at a certain interest rate. This means that the bank you invest your money in will regularly make payments to you, depending on the rate of interest and the amount invested. This is called simple interest. If you don’t take the money, but keep on putting it back in the bank to enlarge the amount saved, the amount of interest keeps increasing. This is called compound interest.

For example: Mrs Van der Merwe saved while she was still employed, and on her retirement she had R150 000 in the bank. This she invested at an interest rate of 11% per annum. Every month the bank pays her one–twelfth of her annual interest. The interest comes to R16 500 per year, so she gets R1 375 per month.

4.1 Mrs Van der Merwe, whose investments we looked at before, now inherits an amount of R95 000. She invests this, this time at an interest rate of 11,5% per annum. The interest is again paid out to her every month. Mrs Van der Merwe also receives a monthly pension of R3 100 from the pension fund of her previous employer. What is the total amount she receives every month?

5 Cars or furniture are often bought on hire purchase. This is a special type of loan for buying large items. It is convenient, but the interest rate is high, the goods have to be insured, a large deposit is required, the repayments are high and the full amount has to be paid within a certain period or the goods can be repossessed. This kind of loan is only given to people who have a fixed job, and then the maximum loan is determined by how much you earn to be sure that you can meet the repayments. An example is when someone wants to buy a new car. She has a steady job, and she has already saved R3 800. The salesman accepts her old car, which he values at R4 100, as part of the deposit. To buy a car costing R70 800,00 she will have to pay about R1 800 per month for 54 months before the car is her property.

5.1 What is the total amount of money she will have paid at the end of the 54 months?

5.2 Say she gets a loan from the bank at a rate of 18%, sells her old car at R4 000 and uses this and her savings to pay the R70 800 for the new car. She pays the bank loan off at a rate of R1 800 per month. What is the total cost of the car at the end of her loan repayments?

6 You have to have money in a foreign currency when you travel overseas. If you want to visit America, you have to exchange your rand for dollars. The amount of rand you have to pay for one dollar fluctuates from day to day. It has been as low as R1,50 in the past, and recently it was R13,80. This relationship between two currencies is called the exchange rate. An American tourist in South Africa paying about R35 for a hamburger, chips and cool drink, can calculate that the meal will cost him about $3,50 if the exchange rate is R10,00 per dollar.

6.1 How many British pounds (£) will a visitor from England pay for the same meal, if the rand–pound exchange rate is 14,85?

end of CLASS WORK

HOMEWORK ASSIGNMENT

1 Find out what the turnover of a business is. Describe it and give an example.

2 Set up an improved budget for the Jacobs family, and decide how the rest of the income is to be spent. Think carefully about possible expenses not on the list in the question.

3 Someone borrows R12 000 at 11% per annum. After the first month she repays R900 month. In your opinion, how many months will it take her to repay the full amount? Show all your working neatly.

4 If you win R3 million in the Lotto and you invest it at 10,5% per annum, how much interest can you expect to receive every year? And monthly? And weekly? And daily? And how much do you still have in the bank? Round your answers to the nearest rand.

5 If you don’t want to borrow money for a car, but you can save R1 500 per month (at an annual interest rate of 13,5%) until you have enough to pay R66 000 for the car of your choice; about how long will it take you?

6 You are on holiday in America, and you want to join a tour group to Disney World. They offer a six–day, all–inclusive tour package for $1 740. The current exchange rate is R9,55 per dollar. Determine the rand amount a tour like this will set you back.

end of HOMEWORK ASSIGNMENT

Assessment

Financial calculations ω

 good  average  not so good

Assessment

Memorandum

TEST

1. A toy shop:

Calculate the net income from the following information, and say whether it is a profit or a loss.

Expenses: Hiring shop: R1 450

Water and electricity: R380

Telephone: R675

Staff salaries: R7 530

Purchases of toys from wholesaler: R67 550

Packaging material: R1 040

Income from sales: R92 406

2. Joey borrows R780 for six months from his dad to fix his bicycle. His dad requires 8% interest per year. What is the sum of money Joey pays back after six months?

3. You receive a bequest of R12 000 from an aunt. But you have to wait five years until you are 19 before receiving it. In the meantime it is invested at 13,5% per annum compounded. What sum do you receive after five years?

4. The rand-euro exchange rate is 8,75. How many rand do you have to exchange if you need 11 500 euros for a holiday in Europe?

Memorandum

1. Net Income = Total Income – Total Expenses = R92 406 – R78 625 = R13781

and this is a profit.

2. For one year the interest comes to R62,40. For six months he owes his dad R811,20 in total.

3. After one year there is R13 620 in the bank.

After two years: R15458,70

After three years: R17 545, 62…

After four years: R19 914,28…

After five years: R22 602,71 rounded to the nearest cent

4. Rand = 8,75 × 11 500 = R100 625

CLASS WORK

1.1.1 Net income = (36 000 + 1 250 + 9 500 ) – 49 000 = –2 250 ( R2 250 loss )

1.1.2 (85 000 + 95 000 + 63 550) – (120 560 + 15 030 + 55 250) = 52 710 rand profit

1.1.3 Loss = R1 100

2.1 There is no right or wrong answer – it is the process that matters.

3.1 R3 972,50

4. The last example (Kevin) is actually more than compound interest. It illustrates the mechanism of an annuity – a popular saving mechanism. It can be taught as enrichment.

When learners learn about common factors, they will appreciate the pattern found in compound interest.

4.1 1 375 + 3 100 + 910,42 = R5 385,42

5.1 About R105 100

5.2 About r R85 000

6.1 £2,36

HOMEWORK ASSIGNMENT

1. Turnover is the total amount made from sales, before any deductions (gross amount).

2. Judge the process and not the answer.

3. 15 months (the amount in the 15^th month is less).

4. Annually: R315 000; monthly: R26 250; weekly: R6 058; daily: R865

5. A little less than two years (in two years she saves nearly R70 000).

6. R16 617