QSC 131 Worksheet 2 03 March - 07 March 1. How long will it take for an investment of R16 000 to earn total interest of R2860 if it attracts a simple interest rate of \( 3.25 \% \) per annum? 2. A loan company lends a customer R500 and states that it must be repaid at the end of the month, when R560 will be due. What annual simple interest is the company charging? 3. You have R15000 to invest today at \( 7 \% \) interest compounded annually. a) Find how much you will have accumulated in the account at the end of i) 3 years; ii) 6 years; and iii) 9 years. b) Use your findings in part (a) to calculate the amount of interest earned in i) the first 3 years (year 1 to 3 ); ii) the second 3 years (year 4 to 6 ) iii) the third 3 years (year 7 to 9 ). c) Compare and contrast your findings in part (b). Explain why the amount if interest earned increases in each succeeding 3 -year period. 4. The postmaster wants to retire on his \( 65^{\text {th }} \) birthday with R1 000000 from an investment he is about to make in his bank on his \( 45^{\text {th }} \) birthday. If the bank pays an interest rate of \( 6 \% \) per annum, compounded daily, how much must the postmaster invest now? 5. R25 000 is invested at an interest rate of \( 12 \% \) for 6 years. Compare the interest earned if interest is compounded i) annually ii) semi-annually iii) quarterly iv) monthly and v) daily Which is the most favourable to the investor? Why do you think this is? 6. Wendy invests R7800 in a savings account and the bank offers interest at a rate of \( 4.25 \% \) p.a. simple interest for the first year, and thereafter the investment earns \( 9 \% \) p.a. compounded weekly. a) How much total interest will Wendy have earned 5 years after the original investment? b) What would be the effective annual rate of interest earned in the fifth year? 7. In January 2019, Bongani invested R30,000 in an account with interest compounded weekly. What annual interest rate (compounded weekly) would allow Bongani's investment to double by the end of December 2025? Give your answer correct to one decimal place 8. A doctor invests R100 000 in a bank that pays a nominal interest rate of \( 8 \% \) per annum, compounded quarterly for 3 years, thereafter the interest jumps from \( 8 \% \) to \( 10 \% \) but is now compounded semi-annually. a) How much total interest will the doctor have earned 5 years after the original investment? b) What would be the effective annual rate of interest earned in the first year? 9. A teacher invests R6 250 in a bank that pays interest at \( 7 \frac{1}{2} \% \) per annum compounded daily. a) What is the meaning of the term effective annual rate of interest? b) How much total interest will the teacher have earned 5 years after the original investment? c) What would be the effective annual rate of interest earned over the 5 years? 10. Mike invests R3000 in a savings account. He leaves it there for 5 years and finds that the balance is now R3900. What interest rate has he been paid if the interest is compounded semi-annually. 11. A company buys a temperature scanner for R750. The scanner depreciates at a rate of \( 81 / 2 \% \) per annum on a straight line basis. What would be the value of the scanner after 9 months? 12. A shop owner buys a car for his shop. At the end of the fourth year the car had a book value of R120 000. Assuming that the depreciation rate was \( 15.75 \% \) per year using the reducing balance method: i) What was the original price of the car? ii) Find the book value of the car at the end of the \( 7^{\text {th }} \) year. 13. A construction company purchased a truck for R240 000. After 4 years, using the reducing balance method, it had a book value of R111 180. Find: i) The annual rate of depreciation (give answer as percentage correct to 2 decimal places). ii) The book value at the end of 3 years.