5 5.4 Calculate the final amount if $$ R 3200 $$ is invested for 5 years at compound interest. Round off the answer to 2 decimal place $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ QUESTION 6 In this question you are not allowed to use a calculator. SHOW ALL YOUR CALCULATIONS. 6.1 Calculate: $$ 6.1 .1 \quad \frac{-64}{-4 \times-2} $$ $$ \qquad $$ $$ \qquad $$ 6.1 .2 $$ \sqrt{25-16} $$ $$ \qquad $$ $$ \qquad $$ 6.1.3 $$ \sqrt[3]{\sqrt[3]{27}-(-\sqrt{25})}= $$ $$ \qquad $$ $$ \qquad $$ 6.2 Use brackets to evaluate: $$ 30 \div 6+5 \times 2-4 \div 2 $$ $$ \qquad $$ $$ \qquad $$

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**5.4 Compound Interest Calculation**

Given:  
- Principal, $$ P = 3200 $$  
- Time, $$ t = 5 $$ years  
- Assuming an annual interest rate of $$ 5\% $$, so $$ r = 0.05 $$

The compound interest formula is:  
$$
A = P(1+r)^t
$$

Substituting the values we get:  
$$
A = 3200\,(1+0.05)^5 = 3200\,(1.05)^5
$$

Calculating $$ (1.05)^5 $$:  
$$
(1.05)^5 \approx 1.27628
$$

Thus,  
$$
A \approx 3200 \times 1.27628 \approx 4084.10
$$

Rounded to 2 decimal places, the final amount is $$\boxed{4084.10}$$.

---

**6.1 Evaluations Without a Calculator**

**6.1.1** Evaluate:
$$
\frac{-64}{-4 \times -2}
$$

Step 1: Compute the denominator:
$$
-4 \times -2 = 8
$$

Step 2: Divide:
$$
\frac{-64}{8} = -8
$$

Thus, the answer is $$\boxed{-8}$$.

---

**6.1.2** Evaluate:
$$
\sqrt{25-16}
$$

Step 1: Compute inside the square root:
$$
25 - 16 = 9
$$

Step 2: Evaluate the square root:
$$
\sqrt{9} = 3
$$

Thus, the answer is $$\boxed{3}$$.

---

**6.1.3** Evaluate:
$$
\sqrt[3]{\sqrt[3]{27} - (-\sqrt{25})}
$$

Step 1: Compute $$\sqrt[3]{27}$$:
$$
\sqrt[3]{27} = 3
$$

Step 2: Compute $$\sqrt{25}$$:
$$
\sqrt{25} = 5
$$

Step 3: Substitute into the expression:
$$
3 - (-5) = 3 + 5 = 8
$$

Step 4: Evaluate the cube root:
$$
\sqrt[3]{8} = 2
$$

Thus, the answer is $$\boxed{2}$$.

---

**6.2 Expression Evaluation Using Brackets**

Evaluate:  
$$
30 \div 6 + 5 \times 2 - 4 \div 2
$$

First, insertion of brackets to clarify order:
$$
\left(\frac{30}{6}\right) + \left(5 \times 2\right) - \left(\frac{4}{2}\right)
$$

Step 1: Compute each operation:  
$$\frac{30}{6} = 5$$  
$$5 \times 2 = 10$$  
$$\frac{4}{2} = 2$$

Step 2: Combine:  
$$
5 + 10 - 2 = 13
$$

Thus, the answer is $$\boxed{13}$$.
**5.4 Compound Interest Calculation** Investing $$ R 3200 $$ for 5 years at 5% compound interest results in a final amount of $$\boxed{4084.10}$$. --- **6.1 Evaluations Without a Calculator** 1. $$\frac{-64}{-4 \times -2} = -8$$ 2. $$\sqrt{25-16} = 3$$ 3. $$\sqrt[3]{\sqrt[3]{27} - (-\sqrt{25})} = 2$$ 4. $$30 \div 6 + 5 \times 2 - 4 \div 2 = 13$$ Thus, the answers are: 1. $$-8$$ 2. $$3$$ 3. $$2$$ 4. $$13$$

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