Answer :
Sure! Let's break down and solve each part of the question step-by-step:
### 4.1. Show with calculations how the total loan of R279,000 was determined
The total loan value can be found by subtracting the deposit from the cash price of the car.
[tex]\[ \text{Total Loan Value} = \text{Cash Price} - \text{Deposit} \][/tex]
Given:
- Cash Price: [tex]\( R310,000 \)[/tex]
- Deposit: [tex]\( R31,000 \)[/tex]
So,
[tex]\[ \text{Total Loan Value} = R310,000 - R31,000 = R279,000 \][/tex]
### 4.2. Calculate the monthly interest rate
To find the monthly interest rate, we convert the annual interest rate to a monthly rate by dividing by 12.
Given:
- Annual Interest Rate: [tex]\( 12.25\% \)[/tex]
First, convert the annual rate to a decimal by dividing by 100:
[tex]\[ 12.25\% = \frac{12.25}{100} = 0.1225 \][/tex]
Now, divide by 12 to find the monthly rate:
[tex]\[ \text{Monthly Interest Rate} = \frac{0.1225}{12} = 0.01020833 \][/tex]
### 4.3. Express the deposit as a percentage of the cash price
To express the deposit as a percentage of the cash price, we use the formula:
[tex]\[ \text{Deposit Percentage} = \left( \frac{\text{Deposit}}{\text{Cash Price}} \right) \times 100 \][/tex]
Given:
- Deposit: [tex]\( R31,000 \)[/tex]
- Cash Price: [tex]\( R310,000 \)[/tex]
So,
[tex]\[ \text{Deposit Percentage} = \left( \frac{R31,000}{R310,000} \right) \times 100 = \frac{31,000}{310,000} \times 100 = 10\% \][/tex]
### 4.4. Verify whether Nkanyezi's statement is valid
Nkanyezi claims that the total payment including the deposit is three times more than the cash price of the car. We need to verify this claim.
First, calculate the total payment including the deposit:
[tex]\[ \text{Total Payment including Deposit} = \text{Total Payment} + \text{Deposit} \][/tex]
Given:
- Total Payment: [tex]\( R395,352 \)[/tex]
- Deposit: [tex]\( R31,000 \)[/tex]
So,
[tex]\[ \text{Total Payment including Deposit} = R395,352 + R31,000 = R426,352 \][/tex]
Next, find three times the cash price:
[tex]\[ \text{Three times the Cash Price} = 3 \times \text{Cash Price} \][/tex]
Given:
- Cash Price: [tex]\( R310,000 \)[/tex]
So,
[tex]\[ \text{Three times the Cash Price} = 3 \times R310,000 = R930,000 \][/tex]
Now, compare the two values. Nkanyezi's claim is that [tex]\( R426,352 \)[/tex] should be greater than [tex]\( R930,000 \)[/tex].
Clearly,
[tex]\[ R426,352 \not> R930,000 \][/tex]
Therefore, Nkanyezi's claim is not valid.
### 4.5. Is it wise to buy a car for cash or through hire purchase? Give a reason for your answer.
Deciding whether it is wise to buy the car for cash or through hire purchase depends on individual circumstances, but we can provide some guidelines:
- Buying for Cash: If you have the full amount of R310,000 available, buying the car for cash can be advantageous as you avoid paying interest, resulting in overall cost savings. This is a good option if it does not significantly deplete your savings or disrupt your financial plans.
- Hire Purchase: If paying the lump sum is not feasible, hire purchase allows for spreading the cost over time. However, it comes with the downside of paying interest, increasing the total cost of the car. It is a manageable option if monthly budgets can accommodate the monthly payments of R5491 over the 72-month period without financial strain.
In conclusion, the decision depends on the buyer's current financial situation, ability to pay upfront, and comfort with incurring interest over time to manage cash flow. Generally, avoiding interest payments by purchasing for cash, if feasible, is financially wiser.
### 4.1. Show with calculations how the total loan of R279,000 was determined
The total loan value can be found by subtracting the deposit from the cash price of the car.
[tex]\[ \text{Total Loan Value} = \text{Cash Price} - \text{Deposit} \][/tex]
Given:
- Cash Price: [tex]\( R310,000 \)[/tex]
- Deposit: [tex]\( R31,000 \)[/tex]
So,
[tex]\[ \text{Total Loan Value} = R310,000 - R31,000 = R279,000 \][/tex]
### 4.2. Calculate the monthly interest rate
To find the monthly interest rate, we convert the annual interest rate to a monthly rate by dividing by 12.
Given:
- Annual Interest Rate: [tex]\( 12.25\% \)[/tex]
First, convert the annual rate to a decimal by dividing by 100:
[tex]\[ 12.25\% = \frac{12.25}{100} = 0.1225 \][/tex]
Now, divide by 12 to find the monthly rate:
[tex]\[ \text{Monthly Interest Rate} = \frac{0.1225}{12} = 0.01020833 \][/tex]
### 4.3. Express the deposit as a percentage of the cash price
To express the deposit as a percentage of the cash price, we use the formula:
[tex]\[ \text{Deposit Percentage} = \left( \frac{\text{Deposit}}{\text{Cash Price}} \right) \times 100 \][/tex]
Given:
- Deposit: [tex]\( R31,000 \)[/tex]
- Cash Price: [tex]\( R310,000 \)[/tex]
So,
[tex]\[ \text{Deposit Percentage} = \left( \frac{R31,000}{R310,000} \right) \times 100 = \frac{31,000}{310,000} \times 100 = 10\% \][/tex]
### 4.4. Verify whether Nkanyezi's statement is valid
Nkanyezi claims that the total payment including the deposit is three times more than the cash price of the car. We need to verify this claim.
First, calculate the total payment including the deposit:
[tex]\[ \text{Total Payment including Deposit} = \text{Total Payment} + \text{Deposit} \][/tex]
Given:
- Total Payment: [tex]\( R395,352 \)[/tex]
- Deposit: [tex]\( R31,000 \)[/tex]
So,
[tex]\[ \text{Total Payment including Deposit} = R395,352 + R31,000 = R426,352 \][/tex]
Next, find three times the cash price:
[tex]\[ \text{Three times the Cash Price} = 3 \times \text{Cash Price} \][/tex]
Given:
- Cash Price: [tex]\( R310,000 \)[/tex]
So,
[tex]\[ \text{Three times the Cash Price} = 3 \times R310,000 = R930,000 \][/tex]
Now, compare the two values. Nkanyezi's claim is that [tex]\( R426,352 \)[/tex] should be greater than [tex]\( R930,000 \)[/tex].
Clearly,
[tex]\[ R426,352 \not> R930,000 \][/tex]
Therefore, Nkanyezi's claim is not valid.
### 4.5. Is it wise to buy a car for cash or through hire purchase? Give a reason for your answer.
Deciding whether it is wise to buy the car for cash or through hire purchase depends on individual circumstances, but we can provide some guidelines:
- Buying for Cash: If you have the full amount of R310,000 available, buying the car for cash can be advantageous as you avoid paying interest, resulting in overall cost savings. This is a good option if it does not significantly deplete your savings or disrupt your financial plans.
- Hire Purchase: If paying the lump sum is not feasible, hire purchase allows for spreading the cost over time. However, it comes with the downside of paying interest, increasing the total cost of the car. It is a manageable option if monthly budgets can accommodate the monthly payments of R5491 over the 72-month period without financial strain.
In conclusion, the decision depends on the buyer's current financial situation, ability to pay upfront, and comfort with incurring interest over time to manage cash flow. Generally, avoiding interest payments by purchasing for cash, if feasible, is financially wiser.
