Answer :
Certainly! Let's break down each part of the problem and provide a detailed, step-by-step solution for each question.
### 3.1 Peter's Payments
#### 3.1.1 Determine his Monthly payment.
Peter bought clothes worth R2,400 and received a R250 voucher. He spreads the remaining cost over a 6-month account.
1. Subtract the voucher from the total cost:
[tex]\[ 2400 - 250 = 2150 \][/tex]
2. To find the monthly payment, we divide the remaining cost by the number of months (6):
[tex]\[ \text{Monthly Payment} = \frac{2150}{6} \approx 358.33 \][/tex]
Therefore, Peter's monthly payment is approximately R358.33.
#### 3.1.2 Calculate the cost of clothes without VAT.
Peter’s clothes cost R2,400 including VAT. Assume the VAT rate is 15%.
1. Let the cost without VAT be [tex]\( C \)[/tex]. The cost with VAT is:
[tex]\[ C + 0.15C = 2400 \implies 1.15C = 2400 \][/tex]
2. Solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{2400}{1.15} \approx 2086.96 \][/tex]
Therefore, the cost of the clothes without VAT is approximately R2086.96.
### 3.2 Desmond's Account
#### 3.2.1 Define the concept "Opening balance" in this context.
The "Opening balance" refers to the amount of money that is in Desmond's account at the start of the period being considered. In this context, it would be the amount in his account on 1st March 2024, before any transactions for the month have taken place.
#### 3.2.2 Show how the balance of R3653.82 on the 15/03/2024 was calculated.
Starting with the opening balance of R4257.88, we calculate the changes step-by-step:
1. Add the interest [tex]\( M \)[/tex] on 05/03/2024, which results in a balance less than 4257.88
2. Subtract the ATM payment of R749 on 09/03/2024:
[tex]\[ 4383.54 - 749 = 3634.54 \][/tex]
3. Add the account protection plan fee of R19.28 on 15/03/2024:
[tex]\[ 3634.54 + 19.28 = 3653.82 \][/tex]
Thus, the balance on 15/03/2024 was R3653.82.
#### 3.2.3 Determine the value of "M", the interest on 05/03/2024.
The interest [tex]\( M \)[/tex] is the difference between the balance on 05/03/2024 and the opening balance:
[tex]\[ M = 4383.54 - 4257.88 = 125.66 \][/tex]
Thus, the value of [tex]\( M \)[/tex] is R125.66.
#### 3.2.4 The instalment amount is not the same as the 'Amount Due'. Give the reason why the two amounts are not the same.
The 'Instalment' refers specifically to a regular, agreed-upon payment amount, whereas the 'Amount Due' likely includes other charges such as interest, fees (e.g., account protection plan fee, lifestyle membership fee), or any additional purchases made on the account. Therefore, the amount due often exceeds the basic instalment.
#### 3.2.5 Determine the actual amount Desmond Mkhize paid in March 2024.
To find the actual amount Desmond paid in March 2024, we sum the ATM payment, the account protection plan fee, and the lifestyle membership fee:
[tex]\[ 749 + 19.28 + 45.12 = 813.4 \][/tex]
Therefore, Desmond Mkhize's actual payment in March 2024 was R813.40.
Thus, all parts of the problem have been addressed with detailed, step-by-step solutions.
### 3.1 Peter's Payments
#### 3.1.1 Determine his Monthly payment.
Peter bought clothes worth R2,400 and received a R250 voucher. He spreads the remaining cost over a 6-month account.
1. Subtract the voucher from the total cost:
[tex]\[ 2400 - 250 = 2150 \][/tex]
2. To find the monthly payment, we divide the remaining cost by the number of months (6):
[tex]\[ \text{Monthly Payment} = \frac{2150}{6} \approx 358.33 \][/tex]
Therefore, Peter's monthly payment is approximately R358.33.
#### 3.1.2 Calculate the cost of clothes without VAT.
Peter’s clothes cost R2,400 including VAT. Assume the VAT rate is 15%.
1. Let the cost without VAT be [tex]\( C \)[/tex]. The cost with VAT is:
[tex]\[ C + 0.15C = 2400 \implies 1.15C = 2400 \][/tex]
2. Solve for [tex]\( C \)[/tex]:
[tex]\[ C = \frac{2400}{1.15} \approx 2086.96 \][/tex]
Therefore, the cost of the clothes without VAT is approximately R2086.96.
### 3.2 Desmond's Account
#### 3.2.1 Define the concept "Opening balance" in this context.
The "Opening balance" refers to the amount of money that is in Desmond's account at the start of the period being considered. In this context, it would be the amount in his account on 1st March 2024, before any transactions for the month have taken place.
#### 3.2.2 Show how the balance of R3653.82 on the 15/03/2024 was calculated.
Starting with the opening balance of R4257.88, we calculate the changes step-by-step:
1. Add the interest [tex]\( M \)[/tex] on 05/03/2024, which results in a balance less than 4257.88
2. Subtract the ATM payment of R749 on 09/03/2024:
[tex]\[ 4383.54 - 749 = 3634.54 \][/tex]
3. Add the account protection plan fee of R19.28 on 15/03/2024:
[tex]\[ 3634.54 + 19.28 = 3653.82 \][/tex]
Thus, the balance on 15/03/2024 was R3653.82.
#### 3.2.3 Determine the value of "M", the interest on 05/03/2024.
The interest [tex]\( M \)[/tex] is the difference between the balance on 05/03/2024 and the opening balance:
[tex]\[ M = 4383.54 - 4257.88 = 125.66 \][/tex]
Thus, the value of [tex]\( M \)[/tex] is R125.66.
#### 3.2.4 The instalment amount is not the same as the 'Amount Due'. Give the reason why the two amounts are not the same.
The 'Instalment' refers specifically to a regular, agreed-upon payment amount, whereas the 'Amount Due' likely includes other charges such as interest, fees (e.g., account protection plan fee, lifestyle membership fee), or any additional purchases made on the account. Therefore, the amount due often exceeds the basic instalment.
#### 3.2.5 Determine the actual amount Desmond Mkhize paid in March 2024.
To find the actual amount Desmond paid in March 2024, we sum the ATM payment, the account protection plan fee, and the lifestyle membership fee:
[tex]\[ 749 + 19.28 + 45.12 = 813.4 \][/tex]
Therefore, Desmond Mkhize's actual payment in March 2024 was R813.40.
Thus, all parts of the problem have been addressed with detailed, step-by-step solutions.
