6. Calculate the final amount if R8 500 is invested for 5 years at a compound interest rate of \( 7 \% \) p.a. (Round off your answer to the nearest cent.) 7. Calculate the following without using a calculator: \( 7.1 \quad 17-9+3-5 \) \( 7.2 \quad-22-(-16) \) \( 7.3 \quad 9 \times(-4) \div(-3) \) \( 7.4 \quad-10+7 \times(-2) \) \( 7.5 \quad-20 \div 5+(-6) \times(-7) \) 8. Calculate the following without using a calculator: \( 8.1 \quad-3^{2}+(-3)^{3} \) \( 8.2 \quad \sqrt{144}-\sqrt[3]{-125} \) Calculate the following without using a calculator. Show your work. \( 9.1 \quad 1 \frac{3}{4}+2 \frac{7}{8}-4 \frac{1}{2} \) \( 9.2 \quad 2 \frac{1}{5} \times 1 \frac{3}{7} \div 7 \frac{1}{3} \) \( 9.3 \quad\left(1 \frac{1}{4}\right)^{2}+\left(-\frac{1}{2}\right)^{3} \) \( 9.4 \quad \sqrt{1 \frac{9}{16}} \times \sqrt[3]{-\frac{8}{125}} \)

Calculate the value by following steps: - step0: Calculate: \(\frac{-20}{5}+\left(-6\right)\left(-7\right)\) - step1: Remove the parentheses: \(\frac{-20}{5}-6\left(-7\right)\) - step2: Divide the terms: \(-4-6\left(-7\right)\) - step3: Multiply the numbers: \(-4+42\) - step4: Add the numbers: \(38\) Calculate or simplify the expression \( -22-(-16) \). Calculate the value by following steps: - step0: Calculate: \(-22-\left(-16\right)\) - step1: Remove the parentheses: \(-22+16\) - step2: Add the numbers: \(-6\) Calculate or simplify the expression \( 8500*(1+0.07)^5 \). Calculate the value by following steps: - step0: Calculate: \(8500\left(1+0.07\right)^{5}\) - step1: Add the numbers: \(8500\times 1.07^{5}\) - step2: Convert the expressions: \(8500\left(\frac{107}{100}\right)^{5}\) - step3: Simplify: \(8500\times \frac{107^{5}}{100^{5}}\) - step4: Rewrite the expression: \(100\times 85\times \frac{107^{5}}{100^{5}}\) - step5: Reduce the numbers: \(85\times \frac{107^{5}}{100^{4}}\) - step6: Rewrite the expression: \(5\times 17\times \frac{107^{5}}{100^{4}}\) - step7: Rewrite the expression: \(5\times 17\times \frac{107^{5}}{25^{4}\times 4^{4}}\) - step8: Rewrite the expression: \(5\times 17\times \frac{107^{5}}{5^{8}\times 4^{4}}\) - step9: Reduce the numbers: \(17\times \frac{107^{5}}{5^{7}\times 4^{4}}\) - step10: Multiply the fractions: \(\frac{17\times 107^{5}}{256\times 5^{7}}\) Calculate or simplify the expression \( (7/4)+(23/8)-(9) \). Calculate the value by following steps: - step0: Calculate: \(\frac{7}{4}+\frac{23}{8}-9\) - step1: Reduce fractions to a common denominator: \(\frac{7\times 2}{4\times 2}+\frac{23}{8}-\frac{9\times 4\times 2}{4\times 2}\) - step2: Multiply the numbers: \(\frac{7\times 2}{8}+\frac{23}{8}-\frac{9\times 4\times 2}{4\times 2}\) - step3: Multiply the numbers: \(\frac{7\times 2}{8}+\frac{23}{8}-\frac{9\times 4\times 2}{8}\) - step4: Transform the expression: \(\frac{7\times 2+23-9\times 4\times 2}{8}\) - step5: Multiply the numbers: \(\frac{14+23-9\times 4\times 2}{8}\) - step6: Multiply the terms: \(\frac{14+23-72}{8}\) - step7: Calculate: \(\frac{-35}{8}\) - step8: Rewrite the fraction: \(-\frac{35}{8}\) Calculate or simplify the expression \( -3^2+(-3)^3 \). Calculate the value by following steps: - step0: Calculate: \(-3^{2}+\left(-3\right)^{3}\) - step1: Simplify: \(-3^{2}-3^{3}\) - step2: Evaluate the power: \(-9-3^{3}\) - step3: Evaluate the power: \(-9-27\) - step4: Subtract the numbers: \(-36\) Calculate or simplify the expression \( (11/5)*(10/7)/(22/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{11}{5}\times \frac{10}{7}}{\frac{22}{3}}\) - step1: Multiply the numbers: \(\frac{\frac{22}{7}}{\frac{22}{3}}\) - step2: Multiply by the reciprocal: \(\frac{22}{7}\times \frac{3}{22}\) - step3: Reduce the numbers: \(\frac{1}{7}\times 3\) - step4: Multiply: \(\frac{3}{7}\) Calculate or simplify the expression \( (5/4)^2+(-1/2)^3 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{5}{4}\right)^{2}+\left(\frac{-1}{2}\right)^{3}\) - step1: Rewrite the fraction: \(\left(\frac{5}{4}\right)^{2}+\left(-\frac{1}{2}\right)^{3}\) - step2: Simplify: \(\frac{5^{2}}{4^{2}}-\left(\frac{1}{2}\right)^{3}\) - step3: Evaluate the power: \(\frac{25}{16}-\left(\frac{1}{2}\right)^{3}\) - step4: Evaluate the power: \(\frac{25}{16}-\frac{1}{8}\) - step5: Reduce fractions to a common denominator: \(\frac{25}{16}-\frac{2}{8\times 2}\) - step6: Multiply the numbers: \(\frac{25}{16}-\frac{2}{16}\) - step7: Transform the expression: \(\frac{25-2}{16}\) - step8: Subtract the numbers: \(\frac{23}{16}\) Calculate or simplify the expression \( 9*(-4)/(-3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{9\left(-4\right)}{\left(-3\right)}\) - step1: Remove the parentheses: \(\frac{9\left(-4\right)}{-3}\) - step2: Multiply the terms: \(\frac{36}{3}\) - step3: Reduce the fraction: \(12\) Calculate or simplify the expression \( 17-9+3-5 \). Calculate the value by following steps: - step0: Calculate: \(17-9+3-5\) - step1: Calculate: \(6\) Calculate or simplify the expression \( -10+7*(-2) \). Calculate the value by following steps: - step0: Calculate: \(-10+7\left(-2\right)\) - step1: Multiply the numbers: \(-10-14\) - step2: Subtract the numbers: \(-24\) Calculate or simplify the expression \( \sqrt(1+9/16) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{1+\frac{9}{16}}\) - step1: Add the numbers: \(\sqrt{\frac{25}{16}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{25}}{\sqrt{16}}\) - step3: Simplify the expression: \(\frac{5}{4}\) Let's solve the problems step by step. ### 6. Compound Interest Calculation To calculate the final amount \( A \) when \( P \) is invested at a compound interest rate \( r \) for \( t \) years, we use the formula: \[ A = P(1 + r)^t \] Where: - \( P = 8500 \) - \( r = 0.07 \) - \( t = 5 \) Calculating: \[ A = 8500(1 + 0.07)^5 \] Now, let's compute this value: \[ A = 8500(1.07)^5 \] Calculating \( (1.07)^5 \): \[ (1.07)^5 \approx 1.402552 \] Now, substituting back: \[ A \approx 8500 \times 1.402552 \approx 11921.69 \] Thus, the final amount is approximately **R 11,921.69**. ### 7. Basic Arithmetic Calculations #### 7.1 \( 17 - 9 + 3 - 5 \) \[ 17 - 9 = 8 \\ 8 + 3 = 11 \\ 11 - 5 = 6 \] Final result: **6** #### 7.2 \( -22 - (-16) \) \[ -22 + 16 = -6 \] Final result: **-6** #### 7.3 \( 9 \times (-4) \div (-3) \) \[ 9 \times (-4) = -36 \\ -36 \div (-3) = 12 \] Final result: **12** #### 7.4 \( -10 + 7 \times (-2) \) \[ 7 \times (-2) = -14 \\ -10 - 14 = -24 \] Final result: **-24** #### 7.5 \( -20 \div 5 + (-6) \times (-7) \) \[ -20 \div 5 = -4 \\ (-6) \times (-7) = 42 \\ -4 + 42 = 38 \] Final result: **38** ### 8. More Calculations #### 8.1 \( -3^2 + (-3)^3 \) \[ -3^2 = -9 \\ (-3)^3 = -27 \\ -9 - 27 = -36 \] Final result: **-36** #### 8.2 \( \sqrt{144} - \sqrt[3]{-125} \) \[ \sqrt{144} = 12 \\ \sqrt[3]{-125} = -5 \\ 12 - (-5) = 12 + 5 = 17 \] Final result: **17** ### 9. Mixed Numbers and Fractions #### 9.1 \( 1 \frac{3}{4} + 2 \frac{7}{8} - 4 \frac{1}{2} \) Convert to improper fractions: \[ 1 \frac{3}{4} = \frac{7}{4}, \quad 2 \frac{7}{8} = \frac{23}{8}, \quad 4 \frac{1}{2} = \frac{9}{2} = \frac{36}{8} \] Now calculate: \[ \frac{7}{4} + \frac{23}{8} - \frac{36}{8} = \frac{14}{8} + \frac{23}{8} - \frac{36}{8} = \frac{14 + 23 - 36}{8} = \frac{1}{8} \] Final result: **\(\frac{1}{8}\)** #### 9.2 \( 2 \frac{1}{5} \times 1 \frac{3}{7} \div 7 \frac{1}{3} \) Convert to improper fractions: \[ 2 \frac{1}{5} = \frac{11}{5}, \quad 1 \frac{3}{7} = \frac{10}{7}, \quad 7 \frac{1}{3} = \frac{22}{3} \] Now calculate: \[ \frac{11}{5} \times \frac{10}{7} \div \frac{22}{3} = \frac{11 \times 10}{5 \times 7} \times \frac{3}{22} = \frac{330}{770} = \frac{33}{77} = \frac{3}{7} \] Final result: **\(\frac{3}{7}\)** #### 9.3 \( \left(1 \frac{1}{4}\right)^{2} + \left(-\frac{1}{2}\right)^{3} \) Convert to improper fractions: \[ 1 \frac{1}{4} = \frac{5}{4} \] Now calculate: \[ \left(\frac{5}{4}\right)^{2} + \left(-\frac{1}{2}\right)^{3} = \frac{25}{16} - \frac{1}{8} = \frac{25}{16} - \frac{2}{16} = \frac{23}{16} \] Final result: **\(\frac{23}{16}\)** #### 9.4 \( \sqrt{1 \frac{9}{16}} \times \sqrt[3]{-\frac{8}{125}} \) Convert to improper fractions: \[ 1 \frac{9}{16} = \frac{25}{16} \] Now calculate: \[ \sqrt{\frac{25}{16}} \times \sqrt[3]{-\frac{8}{125}} = \frac{5}{4} \times -\frac{2}{5} = -\frac{1}{2} \] Final result: **\(-\frac{1}{2}\)** ### Summary of Results - **6:** R 11,921.69 - **7.1:** 6 - **7.2:** -6 - **7.3:** 12 - **7.4:** -24 - **7.5:** 38 - **8.1:** -36 - **8.2:** 17 - **9.1:** \(\frac{1}{8}\) - **9.2:** \(\frac{3}{7}\) - **9.3:** \(\frac{23}{16}\) - **9.4:** \(-\frac{1}{2}\)