Maths Worksheet - Loans

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 31st March 2009 Financial Mathematics – Loans 1. Mr and Mrs Mosepele are newly-married and buy a house for R35 000. They pay R50 000 in cash and take out a home loan for the balance. The interest on the loan is calculated at 8,5% p.a. compounded monthly. a) Calculate the monthly repayments on the loan if the loan is repaid over 30 years. b) How much would they have to repay each month if they decided to repay the loan over 20 years? c) Calculate how much money would be paid in total in each case to repay the loan. 2. Freeda buys a large house with 5 bedrooms. She plans to occupy one room herself and let the other rooms to tenants. She expects that the rental will cover the loan repayments on her house. She takes out a loan of R550 000. The interest on the loan is 8% p.a. compounded monthly. How much does she charge each tenant if the house is to be repaid over 20 years? 3. Thabo starts his own band and buys sound equipment for R30 000. He pays R5 000 in cash and takes out a bank loan for the balance. Calculate the monthly repayments if he repays the loan over three years. The interest rate is 8,2% p.a. compounded monthly. 4. a) Mr Ndlovu buys a bakkie for his business. The bakkie cost him R120 000. He pays 20% in cash and the balance is paid using a bank loan. The interest is 11% p.a. compounded monthly. Calculate the monthly repayments if he repays the loan over four years. b) Determine the balance on the loan after 18 months immediately after his payment. 5. Thenjiwe deposits R12 000 in a savings account which gives an interest rate of 7,2% p.a. compounded monthly. Her savings grew to R17 181,47 over a period of time before she decided to withdraw the money. Calculate how long the Thenjiwe had her money invested. Give your answers in years. 6. Thami dreamed of becoming a millionaire. When he was 30 years old, he invested R200 000 with an investment company. If the interest rate was 8,5% p.a. compounded monthly, how old was he when he achieved his dream? Give your answer correct to the nearest year.

Dear Mr Jones, Do you need to borrow money urgently? You could have instant cash in your hand tomorrow. You have been selected to receive this offer of a loan from FSP. Whether you want to add value to your home with some renovation, or spoil yourself to a dream holiday, instant cash up to R25 000 is available to you right now. Your Loan Options Amounts R8 000 R16 000 R20 000 R25 000

24 months R500 R960 R1 183 R1 479

36 months R388 R737 R905 R1 132

48 months R333 R626 R767 R958

60 months R300 R560 R683 R854

Use this handy installment table to choose the loan that will suit your budget and circumstances. Find the loan amount you need and choose the repayment period that offers you a monthly repayment you feel comfortable with. • Choice of loan term – up to 5 years to repay your loan! • Fixed interest rate – for the full term of your loan! • Cash to use as you choose – for anything that is important to you! 7. Read the advertisement from FSP and answer the questions below. a) Mr Jones takes out a R25 000 loan from FSP for his dream holiday. Calculate how much money he will have to pay if he decides to repay the loan over five years. b) How much interest does Mr Jones pay? c) Use the simple interest formula to determine the rate of simple interest per annum that is being charged over five years.

The diagram shows how a pyramid scheme works. Each investor pays R5 000 and recruits two other investors. Once he recruits 2 other investors he is refunded his R5 000 and the other R5 000 is shared by the investors above him in the pyramid. `

8. If the four investors on level 3 have all successfully recruited 2 new members each, determine how much profit each of the investors on levels 1 and 2 in the pyramid will receive. 9. Suppose all the investors on level 4 have recruited 2 new members each. a) How many new investors will be added to the scheme on level 5? b) How much money in total will be available as profit for the investors on levels 1, 2 and 3? c) Determine the amount of profit that each investor in the pyramid above level 4 receives at this stage. d) Calculate the total profit received by each investor on levels 1, 2 and 3 once the 5th level of the pyramid has been completed. 10. Explain why this pyramid will collapse, and which of the investors will lose their money.