5. An Investor bought US dollars for R100000 at an exchange rate of I USS - R8,17. Seventeen months later he sells the US dollars at an exchange rate of 1 USS $$ = $$ R6,93. 5.1 Calculate the value of the initial investment in USS. 5.2 Calculate the amount he received in rand when he sold the dollars. 5.3 State whether the investor made a profit or a loss. 5.4 Calculate the amount of the profit or loss. Use the conversion rate 10,6 Kenyan shillings is equal to 1 South African rand to convert: 6.1 R30 into shillings 6.2 S30 shillings into rands.

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Let's break down the problem step by step.

### 5.1 Calculate the value of the initial investment in USD.

The initial investment in rand is R100,000, and the exchange rate is 1 USD = R8.17. To find the value in USD, we can use the formula:

$$
\text{USD} = \frac{\text{Rand}}{\text{Exchange Rate}}
$$

Substituting the known values:

$$
\text{USD} = \frac{100000}{8.17}
$$

### 5.2 Calculate the amount he received in rand when he sold the dollars.

After 17 months, the exchange rate is 1 USD = R6.93. The amount received in rand can be calculated as:

$$
\text{Rand Received} = \text{USD} \times \text{New Exchange Rate}
$$

Substituting the value of USD from the previous calculation:

$$
\text{Rand Received} = \left(\frac{100000}{8.17}\right) \times 6.93
$$

### 5.3 State whether the investor made a profit or a loss.

To determine if the investor made a profit or a loss, we compare the initial investment in rand (R100,000) with the amount received in rand after selling the dollars.

### 5.4 Calculate the amount of the profit or loss.

The profit or loss can be calculated as:

$$
\text{Profit/Loss} = \text{Rand Received} - \text{Initial Investment}
$$

Now, let's perform the calculations for 5.1 and 5.2 first.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{100000}{8.17}$$
- step1: Convert the expressions:
  $$\frac{100000}{\frac{817}{100}}$$
- step2: Multiply by the reciprocal:
  $$100000\times \frac{100}{817}$$
- step3: Multiply:
  $$\frac{100000\times 100}{817}$$
- step4: Multiply:
  $$\frac{10000000}{817}$$
Calculate or simplify the expression $$ (100000 / 8.17) * 6.93 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{100000}{8.17}\right)\times 6.93$$
- step1: Divide the numbers:
  $$\frac{10000000}{817}\times 6.93$$
- step2: Convert the expressions:
  $$\frac{10000000}{817}\times \frac{693}{100}$$
- step3: Multiply the numbers:
  $$\frac{69300000}{817}$$
### 5.1 Value of the initial investment in USD

The value of the initial investment in USD is approximately:

$$
\text{USD} \approx 12239.90
$$

### 5.2 Amount received in rand when he sold the dollars

The amount received in rand when he sold the dollars is approximately:

$$
\text{Rand Received} \approx 84822.52
$$

### 5.3 Determine if the investor made a profit or a loss

Now, we compare the amount received in rand (R84,822.52) with the initial investment (R100,000):

- Initial Investment: R100,000
- Amount Received: R84,822.52

Since R84,822.52 is less than R100,000, the investor made a **loss**.

### 5.4 Calculate the amount of the profit or loss

The loss can be calculated as:

$$
\text{Loss} = \text{Initial Investment} - \text{Rand Received}
$$

Substituting the values:

$$
\text{Loss} = 100000 - 84822.52
$$

Now, let's calculate the loss.
Calculate the value by following steps:
- step0: Calculate:
  $$100000-84822.52$$
- step1: Subtract the numbers:
  $$15177.48$$
### 5.4 Amount of the loss

The amount of the loss is approximately:

$$
\text{Loss} \approx 15177.48
$$

### Summary of Results
- **5.1** Value of the initial investment in USD: **$12,239.90**
- **5.2** Amount received in rand when he sold the dollars: **R84,822.52**
- **5.3** The investor made a **loss**.
- **5.4** Amount of the loss: **R15,177.48**

---

Now, let's move on to the conversion of rand to Kenyan shillings and vice versa.

### 6.1 Convert R30 into shillings

Given the conversion rate of 10.6 Kenyan shillings = 1 South African rand, we can calculate:

$$
\text{Shillings} = \text{Rand} \times 10.6
$$

Substituting R30:

$$
\text{Shillings} = 30 \times 10.6
$$

### 6.2 Convert S30 shillings into rands

To convert shillings back to rand, we can use the inverse of the conversion rate:

$$
\text{Rand} = \frac{\text{Shillings}}{10.6}
$$

Substituting S30:

$$
\text{Rand} = \frac{30}{10.6}
$$

Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$30\times 10.6$$
- step1: Multiply the numbers:
  $$318$$
Calculate or simplify the expression $$ 30 / 10.6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{30}{10.6}$$
- step1: Convert the expressions:
  $$\frac{30}{\frac{53}{5}}$$
- step2: Multiply by the reciprocal:
  $$30\times \frac{5}{53}$$
- step3: Multiply:
  $$\frac{30\times 5}{53}$$
- step4: Multiply:
  $$\frac{150}{53}$$
### 6.1 Convert R30 into shillings

The conversion of R30 into Kenyan shillings is:

$$
\text{Shillings} = 30 \times 10.6 = 318
$$

### 6.2 Convert S30 shillings into rands

The conversion of S30 shillings back into rand is approximately:

$$
\text{Rand} \approx 2.83
$$

### Summary of Conversion Results
- **6.1** R30 is equivalent to **318 Kenyan shillings**.
- **6.2** S30 is approximately equivalent to **R2.83**.

If you have any further questions or need additional calculations, feel free to ask!
- **5.1** Initial investment in USD: **$12,239.90** - **5.2** Amount received in rand after selling: **R84,822.52** - **5.3** The investor made a **loss**. - **5.4** Amount of the loss: **R15,177.48** - **6.1** R30 is equivalent to **318 Kenyan shillings**. - **6.2** S30 is approximately equivalent to **R2.83**.

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