GRADE 9 FINANCIAL MATHS INVESTMENTS AND INTEREST When you borrow money you have to pay interest. This means that you have to pay back more than you have borrowed. One way of making money is through investments. When you invest money, for example, in unit trusts, for a period of 5 or 10 years, the money increases because of the interest added during this period. In order to calculate the amount interest owed or earned, you have to understand how to work with percentages. Percentages are all around us and it is important to understand exactly what they mean. EXERCISE 1: Practice with percentages (Show working) 1. Nosisi s little sister has 7 out of the 10 different Barbie dolls on the market. What percentage of the Barbie doll range does she have? 2. Write each of the following as a percentage: EXAMPLE: 3 out of 7 3 100 x 42.86% 7 1 2.1 1 out of 5 2.2 63 out of 100 2.3 33 out of 150 3. Write each per cent as a fraction or mixed number as a decimal. 28 EXAMPLE: 28% 0. 28 100 3.1 21% 3.2 35% 3.3 48% 3.4 72% 3.5 120% 4. Calculate each of the following:
EXAMPLE: 15% of R920 15 920 x R138 100 1-1 - 4.1 30% of 100 4.2 16% of 72 4.3 40% of 5 4.4 80% of 5 5. Explain the following: The standard tip for a waiter is about 15%. Give an example. 6. For your final mark, your teacher might combine your examination mark and your term mark based on homework, assignments and other assessments in your portfolios, using an equation like this one: 40% of term mark + 60% exam mark = final mark Suppose your term mark is 84% and your exam mark is 50%. What will your final mark be? 7. In all of William Shakespeare s writings put together, he used 31 534 words of which 14 356 were used only once. What percentage of the words did he use only once. Round off your answer to one decimal place. 8. Express each reduction as a percentage of the original price: EXAMPLE: A pair of shoes which normally cost R227,00, now sells for R160,00. Express the reduction as a percentage. difference inprice 100 x originalprice 1 227 160 100 x 227 1 29.52%
8.1 An ipod which normally costs 8.2 A pair of Adidas soccer boots which R2 499.95, now sells for for R595 9. A photocopy machine will enlarge a diagram to 142% of its original size. If the diagram has a length of 12cm and a breadth of 8cm, what will the dimensions (size) of the enlargement be? - 2 - EXERCISE 2: Simple Interest and Loans 1. What does to earn interest on money mean? 2. Your aunt is encouraging you to save some of the money you earn from your weekend job. She offers to pay you 10% interest on all the money you save in 2 years. You manage to save R500 over the period of two years. How much will she pay you? Show all your calculations. 3. Your aunt worked out the interest she needed to pay you the following way: S.I. 10 500 2 100 100 3.1 Would it have been incorrect if she had done her calculation the following way? Explain. S.I. 500 10% 2
3.2 What about S.I. 500 0,1 2? - 3 - To calculate simple interest, you multiply the amount of money by the rate of interest (%) earned by time (e.g. years) Formula: S.I. P i n A P(1+ in) A = final amount P = starting amount (Principal) r i rate of interest i 100 n time 4. Use the simple interest formula to answer the following questions: EXAMPLE: R8 000 is taken out as a loan for five years at a simple interest rate of 9,5%p.a. How much money must be repaid at the end of five years? i = 0,095 A = P(1 + i.n) A = 8 000 ( 1 + 0.095 x 5 ) = R11 800 4.1 Calculate the final amount if R200 was invested for 2 years at 6% per annum (per year) simple interest. 4.2 If Lebo decided to invest R12 000 at 5% per annum simple interest for 5 years, How much will be in the account at the end of the 5 years? How much would the interest be? Final amount
EXERCISE 3: Hire purchase, lay-bys and loans and bank charges - 4 - People seldom have enough money to satisfy all their needs and wants, so they have to make choices. Businesses use advertisements to influence our choices and to convince us to spend our money on particular products. 1. Look at these advertisements: Advert 1 Advert 2 Advert 3 Explain how each of the adverts above are designed to convince us to spend our money. Businesses also offer different ways of paying for goods if you are not able to pay cash for them. 2.1 Some shops have a lay-by system. Explain what this means. 2.2 Thombe bought a pair a tennis shoes that cost R242,42 on lay-by. She paid 17,5% deposit and agreed to pay R50 per month until the shoes had been paid for. 2.2.1 How much did she pay as a deposit? 2.2.2 After how long was she able to wear the shoes? 3.1 Some shops have hire-purchase schemes. Explain what hire-purchase is.
3.2 Calculate the difference in the price of a bicycle that costs R795 in cash or R200 deposit and R162 per month over 6 months. - 5-3.3 Jo earns R200 at he weekend by mowing lawns in his neighbourhood. At the moment he has to hire a mower that costs R50 for the weekend. He sees a new mower that costs R1 199 for cash. Hire purchase rates are: R120 deposit and monthly payments of R77 for 18 months. 3.3.1 Calculate the difference between the cash price and the hire purchase price. 3.3.2 Which option is cheaper? 3.3.3 How long will he have to save for if he wants to buy the new mower for cash? EXERCISE 4: Compound interest 1. You win R1 000 in a competition. You deposit the money into a bank account where you will earn interest at a rate of 5% for every year that the money is in the bank. 1.1 How much interest have you earned after 1 year? 1.2 If you don t spend any of that money, how much do you now have in your account? 1.3 How much interest will you earn at the end of the second year? 1.4 If you don t spend any of that money, how much do you now have in your account? 1.5 How much interest will you earn at the end of the third year?
- 6-1.6 If you don t spend any of that money, how much do you now have in your account? 1.7 How much interest will you earn at the end of the fourth year? What you have done is worked out the sum of the interest earned every year. Each year the principal amount changes because the interest from the year before is added to it. This is called COMPOUND INTEREST 1.8 Would your R1 000 be worth the same amount if you earned simple interest for 4 years. Show your calculations. The formula for finding the amount you will receive after earning compound interest is: A P(1 i) n A = final amount P = original amount n = time units r i rate 100 To calculate the amount of interest: I = A P 2. The table alongside shows how an investment of R5 000 grows over a period of 5 years at 6 % compound interest per year. R5 000 investment at 6% interest per year Year Amount 1 5 300 2 3 5 955,08 4 5 2.1 Calculate the amount of money that would be in the bank after two years
- 7-2.2 How much interest would have been earned after 4 years? 2.3 What would the investment be worth after 5 years? 2.4 Using a formula, complete the following: 2.4.1 You are offered 8% simple interest on your R5 000 for 5 years. Would you accept the offer? 2.4.2 Explain why or why not and show all calculations. 3. Calculate the future value on an investment of R6 000 if the interest is compounded annually at a rate of 15% over 10 years. 4. Ntuli deposits R8 000 into a savings account where the interest paid is 9% compounded annually. Calculate how much she will have in her account after 11 years. 5. Mr Morari invests R5 000 at compound interest, calculated at 8% for the first year, 6% for the second year and 5% for the third year. 5.1 How much money will he have in his account at the end of three years?
- 8-5.2 How much interest will he have earned at the end of the third year? 6. What is the difference between the compound interest and simple interest on R200 000 after 3 years at 6% per annum? SUMMARY Simple interest is the interest calculated at the end of the investment period and does not include any interest that might have been earned during that time Compound interest is the sum of the interest amounts earned very year. Each time the principal changes because the interest from the year before is added to it. Exercises 5 and 6 are examples of how interest is earned. However, there are many times when you need to work out interest that is owed. Even if you draw money from your bank in order to pay cash for an item, you will have to pay bank charges!
INFLATION RATE - 9 - Inflation is the continuous increase in the general level of prices over a period of time. DEPRECIATION RATES Depreciation is the loss of value in assets, machinery or equipment through usage or age. Depreciation can be calculated in a number of ways. The two most common methods are: Straight-line depreciation: The depreciation is calculated as a percentage of the original value of the asst each year. This type of depreciation will result in the equipment having no value at all after a period of time. Reducing-balance depreciation: The depreciation is calculated as a percentage of the reduced value of the asset each year, This type of depreciation will ensure that the equipment always has some value at the end of a certain period. The formula for depreciation on a reducing balance is: A=P(1 - i) n A = future value of the equipment P = present value of the equipment n = number of years r i annual rate of depreciation 100 EXAMPLE: The machinery in a factory costs R2,5m. The rate of depreciation is calculated at 18%p.a. on a reducing balance. Calculate the value of the machinery at the end of 10 years. P = R2 500 000 i = 0.18 n = 10 A = P ( 1 i ) n A = 2 500 000 ( 1 0.18 ) 10 = R 343 620
INTERNATIONAL BUSINESS: EXERCISE 5: Exchange rates - 10 - The table below shows what 1 unit of foreign currency will cost in South African rands. Use the table to help you answer the questions that follow the table: Value of South African rand on 18 March 2000 Currency In South African rand Botswana pula 1,925 Indian rupee 0,148 Italian lire 0,0032 New Zealand dollar 3,135 Zimbabwean dollar 0,178 1. A consignment of computers imported from Japan cost 976 000 Japanese yen. How much would the importers have to pay in South African rands? 2. A dealer buys African arts and crafts from Zimbabwe and pays 9 250 Zim$. How much did they cost in rands? 3.1 In Italy, a pair of shoes costs 80 000 lire. How much would you pay for the shoes in rands? 3.2 A shoe shop imports 60 pairs of shoes from Italy and pays 80 000 lire per pair. They are sold for R420 per pair in South Africa. How much profit would the shop make on each pair of shoes if profit = selling price cost price? 4. A painting worth R 20 000 is sold in India. How many Indian rupees would the artist receive for the painting?
- 11-5. A certain model of bakkie is manufactured in South Africa and exported to Botswana at a cost of R84 000. In addition, 21% import tax must be added to the cost price. How much will the bakkie cost in Botswana in pula? 6.1 University fees in Auckland are 5 300 New Zealand $ for one year of study. How much would you have to pay in rands if you planned to study for one year? 6.2 How much would your second year of study cost you ( in rands) if the fees increased by 10%? COMMISSIONS AND RENTALS A wage is paid weekly and is based on an hourly rate. A salary is paid monthly and is calculated on an annual amount. A commission is money that is paid to the seller for the goods, services or property sold. Rental is the money charged for the use of property or the hire of vehicles or goods.