Pension Cell Phones
1. **Problem 2.1.1:** Write down the value of the lump sum payable to beneficiaries in 2022 in words.
- The lump sum payable to beneficiaries in 2022 is R2 592 409.
- In words: Two million five hundred ninety-two thousand four hundred nine.
2. **Problem 2.1.2:** Calculate the retirement benefit for 2023 given it is 2.8% more than 2022's value.
- Given retirement benefit in 2022: R2 836 836.
- Increase percentage: 2.8% = 0.028.
- Formula for increased value: $$\text{New Value} = \text{Old Value} \times (1 + \text{Percentage Increase})$$
- Calculation: $$2\,836\,836 \times (1 + 0.028) = 2\,836\,836 \times 1.028 = 2\,915\,711.41$$
- So, the retirement benefit for 2023 is approximately R2 915 711.41.
3. **Problem 2.2.1:** Determine the ratio of total profit to total income sale of the four cell phones in simplest form.
- Total profit = 3333.16 + 4999.83 + 1166.50 + 549.82 = 10 049.31
- Total cost price = 16 665.72 + 24 999.16 + 5 832.50 + 2 749.17 = 50 246.55
- Total income sale = Total cost price + Total profit = 50 246.55 + 10 049.31 = 60 295.86
- Ratio (profit : income) = 10 049.31 : 60 295.86
- Simplify by dividing both by 10 049.31:
$$1 : \frac{60\,295.86}{10\,049.31} \approx 1 : 6$$
- So, the ratio in simplest form is approximately 1:6.
4. **Problem 2.2.2:** Calculate the VAT exclusive price of Samsung Galaxy A34 5G given selling price including VAT is R6999.
- VAT rate = 15% = 0.15
- Formula: $$\text{VAT Exclusive Price} = \frac{\text{Price including VAT}}{1 + \text{VAT rate}}$$
- Calculation: $$\frac{6999}{1.15} = 6081.74$$
- VAT exclusive price is approximately R6081.74.
5. **Problem 2.2.3:** Calculate the percentage decrease in cost price of Samsung Galaxy S23 ULTRA from 2022 to 2023.
- Old price (2022) = R21 665.83
- New price (2023) = R24 999.16 (given in problem, but user says it costs less this year, so check carefully)
Note: The problem states the cost price in 2023 is R24 999.16, which is higher than 2022's R21 665.83, so this contradicts the statement that it costs less this year. Possibly a typo in the problem or user wants percentage decrease assuming new price is less.
Assuming the new price is less, but given data shows otherwise, so we calculate percentage change (increase or decrease):
- Percentage change formula: $$\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100\%$$
- Calculation: $$\frac{24\,999.16 - 21\,665.83}{21\,665.83} \times 100\% = \frac{3\,333.33}{21\,665.83} \times 100\% \approx 15.38\%$$
- Since the new price is higher, this is a 15% increase, not a decrease.
If the problem intended a decrease, data may be incorrect.
**Final answers:**
- 2.1.1: Two million five hundred ninety-two thousand four hundred nine.
- 2.1.2: R2 915 711.41
- 2.2.1: Ratio of total profit to total income sale is approximately 1:6.
- 2.2.2: VAT exclusive price of Samsung Galaxy A34 5G is approximately R6081.74.
- 2.2.3: Percentage change in cost price of Samsung Galaxy S23 ULTRA is approximately +15% (increase).