Math L2 Module 15

Mathematics NQF Level 2 Downloaded from hlayiso.com *see terms and conditions Mathematics NQF Level 2

Using simple and compound interest in various situations Module 15 Downloaded from hlayiso.com Mathematics NQF Level 2

Learning activity 15.1 Downloaded from hlayiso.com Mathematics NQF Level 2

Click above to play this video. Downloaded from hlayiso.com Learning activity 15.1

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JB1 JB2 Summative assessment Module 15 Downloaded from hlayiso.com Mathematics NQF Level 2

Slide 7 JB1 is this in the right place? Janet Bartlet, 11-Feb-18 JB2 where have slides 6-13 gone? Janet Bartlet, 12-Feb-18 Downloaded from hlayiso.com

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 15

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Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 15

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 15

3. The value of a property is R750 000. If the expected inflation rate over the next five years is 5,5%, calculate: 3.1 the expected value of the property after five years P  750 000; A  ?; n  5; r  5,5% n  r  A  P 1    100  5  5,5   750 000  1    100   R980 220 Downloaded from hlayiso.com Summative assessment – Module 15

3. (continued) 3.2 what the price of the property would have been three years ago if the inflation rate had stayed the same P = ? ; A = 750 000; n  3; r  5,5% n  r  A  P 1    100  3  5,5  750 000  P 1    100  Downloaded from hlayiso.com Summative assessment – Module 15

3. (continued) 3.2 what the price of the property would have been three years ago if the inflation rate had stayed the same (continued) \750 000  P ´ 1,174 750 000 \P = 1,174 = R638 710,25 Downloaded from hlayiso.com Summative assessment – Module 15

Downloaded from hlayiso.com Summative assessment – Module 15

Downloaded from hlayiso.com Summative assessment – Module 15

4. Calculate the final amount if R600 is invested at: 4.1 7,5% compound interest calculated annually for five years P  600; A  ?; n  5; r  7,5% n  r  A  P 1    100  5  7,5   600  1    100   R861,38 Downloaded from hlayiso.com Summative assessment – Module 15

4. Calculate the final amount if R600 is invested at: 4.2 9% simple interest calculated annually for five years P  600; A  ?; n  5; r  7,5%  r  A  P 1  ( n)   100   9   600  1  (5)   100   R870,00 Downloaded from hlayiso.com Summative assessment – Module 15

5. Phuti invests R7 200. At what rate must he invest the money to have R10 000 after five years if interest is calculated at: 5.1 simple interest annually? P = 7 200 ; A = 10 000; n  5; r  ?  r  A  P 1  ( n)   100   r  10 000  7 200  1  (5)   100  10 000  1  0, 05r 7 200 Downloaded from hlayiso.com Summative assessment – Module 15

5. Phuti invests R7 200. At what rate must he invest the money to have R10 000 after five years if interest is calculated at: 5.1 simple interest annually? (continued) \1,3889  1  0, 05r 0,3889  0, 05r 0, 3889 \r  0, 5  7, 78% Downloaded from hlayiso.com Summative assessment – Module 15

5. (continued) 5.2 compound interest annually? P = 7 200; A = 10 000; n  5; r  ? n  r  A  P 1    100  5  r  10 000  7 200  1    100  5 10 000  r   1   7 200  100  Downloaded from hlayiso.com Summative assessment – Module 15

5. (continued) 5.2 compound interest annually? (continued) 1 r 5 \1   (1,3889) 100 100  r  100 ´ 1, 0679 100  r  106, 79 \ r  6, 79% Downloaded from hlayiso.com Summative assessment – Module 15

6. Calculate the amount that must be invested to have R10 000 after five years if interest is calculated annually at: 6.1 8% simple interest P = ? ; A = 10 000; n  5; r  8%  r  A  P 1  ( n)   100   8  10 000  P 1  (5)   100  Downloaded from hlayiso.com Summative assessment – Module 15

6. Calculate the amount that must be invested to have R10 000 after five years if interest is calculated annually at: 6.1 8% simple interest (continued) \10 000  P(1,4) 10 000 P(1,4)  1, 4 1, 4 \ P = R7 142,86 Downloaded from hlayiso.com Summative assessment – Module 15

6. (continued) 6.2 8% compound interest P = ? ; A = 10 000; n  5; r  8% n  r  A  P 1    100  5  8  10 000  P 1    100  Downloaded from hlayiso.com Summative assessment – Module 15

6. (continued) 6.2 8% compound interest (continued) \10 000  P(1,469) 10 000 \P = 1, 469  R6 805,83 Downloaded from hlayiso.com Summative assessment – Module 15

7. Thabo paid R5 000 to become a partner in a scrap metal yard. After ten years he sold his share for R10 000. Calculate the bank interest rate that would provide the same return if interest were compounded annually at a: 7.1 simple interest rate A  10 000; P  5 000; n  10; r  ?  r  A  P 1  ( n)   100   r  10 000  5 000  1  (10)   100  Downloaded from hlayiso.com Summative assessment – Module 15

7. Thabo paid R5 000 to become a partner in a scrap metal yard. After ten years he sold his share for R10 000. Calculate the bank interest rate that would provide the same return if interest were compounded annually at a: 7.1 simple interest rate (continued)  r  \ 2  1    10  \ r = 10% Downloaded from hlayiso.com Summative assessment – Module 15

7. (continued) 7.2 compound interest rate A  10 000; P  5 000; n  10; r  ? n  r  A  P 1    100  10  r  10 000  5 000  1    100  10  r  2  1    10  Downloaded from hlayiso.com Summative assessment – Module 15

7. (continued) 7.2 compound interest rate (continued) 1 10 r \2  1 100 r 1, 072  1  100 7, 2%  r \ r = 7,2% Downloaded from hlayiso.com Summative assessment – Module 15

8. Khanyile invests an amount of R1 200 at 10% per annum, simple interest. Bongi invests an amount of R600 at 24%, simple interest. When will both investments have the same accumulated value? Khanyile A  P éë1 in ùû  1 200 éë1 ( 0,1) n ùû  1 200 120n A  1 200  120n Downloaded from hlayiso.com Summative assessment – Module 15

8. (continued) Bongi A  P éë1 in ùû  600 éë1 ( 0,24 ) n ùû  600  144n A  600  144n Downloaded from hlayiso.com Summative assessment – Module 15

8. (continued) For both investments to be the same: A Khanyile = A Bongi 1200 120n  600 144n 1200  600  144n 120n 600  24n 600 \n   25 24 \ Both investments will have the same accumulated Downloaded from hlayiso.com value in 25 years. Summative assessment – Module 15

9. The following table shows the investments of two family members when each of them received their bonuses: NAME AMOUNT INTEREST RATE ON TERM INVESTED OPTION Cyanne R6 000 15% per annum, simple 5 interest years Tahir R6 000 12% per annum, 5 compound interest years Who gained more interest on the investment? Substantiate the answer. Show ALL calculations. Downloaded from hlayiso.com Summative assessment – Module 15

9. (continued) Cyanne A  P éë1 in ùû  6 000 éë1 ( 0,15) ( 5) ùû  6 000 éë1,75ùû  10 500 \ Cyanne received R10 500 after 5 years. Downloaded from hlayiso.com Summative assessment – Module 15

9. (continued) Tahir n A  P éë1 i ùû 5  6 000 éë1 0,12 ùû 5  6 000 éë1,12 ùû  10 574,05 \ Tahir received R10 574,05 after 5 years. Downloaded from hlayiso.com Summative assessment – Module 15

9. (continued) Cyanne Tahir R10 500,00 R10 574,05 \ Tahir gained more interest on the investment. Downloaded from hlayiso.com Summative assessment – Module 15

10. Lesedi invested R6 550 in a savings account. If the interest was compounded annually, calculate the yearly interest rate that Lesedi received if he had R11 543,34 in his account after 5 years. A = 11 543,34; P = 6 550; n = 5 years; r = ? A i  5 1 P 11 543,34  5 1 6 550  0,12 Downloaded from hlayiso.com Summative assessment – Module 15

10. (continued) r  100i  100 ( 0,12 )  12% Lesedi received 12% interest per annum. Downloaded from hlayiso.com Summative assessment – Module 15

11. Determine how long it will take an investment of R70 000 to reach an amount of R103 600 if the simple interest rate is 16%. A = 103 600; P = 70 000; r  16%; n  ? r i 100 16 \i   0,16 100 Downloaded from hlayiso.com Summative assessment – Module 15

11. (continued) AP n Pi 103 600  70 000  ( 70 000 )( 0,16 ) = 3 years \It will take 3 years. Downloaded from hlayiso.com Summative assessment – Module 15

12. Determine the simple interest rate if an investment of R6 000 is worth R10 560 after eight years. A = 10 560; P = 6 000; n = 8 years; r = ? AP i Pn 10 560  6 000  ( 6 000 )(8 )  0,095 Downloaded from hlayiso.com Summative assessment – Module 15

12. (continued) r  100i  100 ( 0,095)  9,5% Interest rate is 9,5% per annum. Downloaded from hlayiso.com Summative assessment – Module 15

Downloaded from hlayiso.com Mathematics NQF Level 2