Answer :
Let's go through each part of the question step-by-step:
### Given Data
- Monthly income: R16,500
- Purchase price of the house: R500,000
- Interest rate: 9% per annum
- Monthly repayments must not exceed 30% of the buyer's gross salary.
- Monthly instalments for different terms:
- 10 years: R6,333.79
- 15 years: R5,071.33
- 20 years: R4,498.63
- 25 years: R4,195.98
- 30 years: R4,023.11
### (a) How much can Mandla spend on a monthly bond repayment?
Mandla can spend up to 30% of his monthly income on a bond repayment:
[tex]\[ \text{Max Monthly Repayment} = 0.30 \times \text{Monthly Income} = 0.30 \times 16,500 = \text{R4,950} \][/tex]
So, Mandla can spend R4,950 on a monthly bond repayment.
### (b) Can Mandla afford to buy a house with a purchase price of R500,000 to be paid over 30 years?
The monthly instalment for a 30-year bond is R4,023.11. We compare this with the maximum monthly repayment Mandla can afford:
[tex]\[ \text{Max Monthly Repayment} = \text{R4,950} \][/tex]
[tex]\[ \text{Monthly Instalment (30 years)} = \text{R4,023.11} \][/tex]
Since R4,023.11 is less than R4,950, Mandla can afford the monthly instalment for a 30-year bond. Hence, Mandla can afford to buy the house with a purchase price of R500,000.
### (c) How much will he repay in interest on the bond over 30 years?
First, we calculate the total repayment amount over 30 years:
[tex]\[ \text{Total Repayment (30 years)} = \text{Monthly Instalment (30 years)} \times 30 \times 12 \][/tex]
[tex]\[ \text{Total Repayment (30 years)} = 4,023.11 \times 30 \times 12 = \text{R1,448,320.71} \][/tex]
Next, the interest repaid is the total repayment amount minus the purchase price:
[tex]\[ \text{Interest Repaid} = \text{Total Repayment (30 years)} - \text{Purchase Price} \][/tex]
[tex]\[ \text{Interest Repaid} = 1,448,320.71 - 500,000 = \text{R948,320.71} \][/tex]
So, Mandla will repay R948,320.71 in interest over 30 years.
### (d) How much will he save if he takes a bond over 20 years instead of 30 years?
First, calculate the total repayment amount for a 20-year bond:
[tex]\[ \text{Total Repayment (20 years)} = \text{Monthly Instalment (20 years)} \times 20 \times 12 \][/tex]
[tex]\[ \text{Total Repayment (20 years)} = 4,498.63 \times 20 \times 12 = \text{R1,079,671.15} \][/tex]
Then, determine the savings by comparing the total repayments for 30 and 20 years:
[tex]\[ \text{Money Saved} = \text{Total Repayment (30 years)} - \text{Total Repayment (20 years)} \][/tex]
[tex]\[ \text{Money Saved} = 1,448,320.71 - 1,079,671.15 = \text{R368,649.56} \][/tex]
So, Mandla will save R368,649.56 if he takes a bond over 20 years instead of 30 years.
### (e) What effect do the increased monthly instalments have on the loan term?
The increased monthly instalments reduce the total cost of the loan by decreasing the term. As the term is reduced, the total amount of interest paid over the life of the loan is also reduced. This is because the principal is repaid more quickly, resulting in less interest accruing over time.
### Given Data
- Monthly income: R16,500
- Purchase price of the house: R500,000
- Interest rate: 9% per annum
- Monthly repayments must not exceed 30% of the buyer's gross salary.
- Monthly instalments for different terms:
- 10 years: R6,333.79
- 15 years: R5,071.33
- 20 years: R4,498.63
- 25 years: R4,195.98
- 30 years: R4,023.11
### (a) How much can Mandla spend on a monthly bond repayment?
Mandla can spend up to 30% of his monthly income on a bond repayment:
[tex]\[ \text{Max Monthly Repayment} = 0.30 \times \text{Monthly Income} = 0.30 \times 16,500 = \text{R4,950} \][/tex]
So, Mandla can spend R4,950 on a monthly bond repayment.
### (b) Can Mandla afford to buy a house with a purchase price of R500,000 to be paid over 30 years?
The monthly instalment for a 30-year bond is R4,023.11. We compare this with the maximum monthly repayment Mandla can afford:
[tex]\[ \text{Max Monthly Repayment} = \text{R4,950} \][/tex]
[tex]\[ \text{Monthly Instalment (30 years)} = \text{R4,023.11} \][/tex]
Since R4,023.11 is less than R4,950, Mandla can afford the monthly instalment for a 30-year bond. Hence, Mandla can afford to buy the house with a purchase price of R500,000.
### (c) How much will he repay in interest on the bond over 30 years?
First, we calculate the total repayment amount over 30 years:
[tex]\[ \text{Total Repayment (30 years)} = \text{Monthly Instalment (30 years)} \times 30 \times 12 \][/tex]
[tex]\[ \text{Total Repayment (30 years)} = 4,023.11 \times 30 \times 12 = \text{R1,448,320.71} \][/tex]
Next, the interest repaid is the total repayment amount minus the purchase price:
[tex]\[ \text{Interest Repaid} = \text{Total Repayment (30 years)} - \text{Purchase Price} \][/tex]
[tex]\[ \text{Interest Repaid} = 1,448,320.71 - 500,000 = \text{R948,320.71} \][/tex]
So, Mandla will repay R948,320.71 in interest over 30 years.
### (d) How much will he save if he takes a bond over 20 years instead of 30 years?
First, calculate the total repayment amount for a 20-year bond:
[tex]\[ \text{Total Repayment (20 years)} = \text{Monthly Instalment (20 years)} \times 20 \times 12 \][/tex]
[tex]\[ \text{Total Repayment (20 years)} = 4,498.63 \times 20 \times 12 = \text{R1,079,671.15} \][/tex]
Then, determine the savings by comparing the total repayments for 30 and 20 years:
[tex]\[ \text{Money Saved} = \text{Total Repayment (30 years)} - \text{Total Repayment (20 years)} \][/tex]
[tex]\[ \text{Money Saved} = 1,448,320.71 - 1,079,671.15 = \text{R368,649.56} \][/tex]
So, Mandla will save R368,649.56 if he takes a bond over 20 years instead of 30 years.
### (e) What effect do the increased monthly instalments have on the loan term?
The increased monthly instalments reduce the total cost of the loan by decreasing the term. As the term is reduced, the total amount of interest paid over the life of the loan is also reduced. This is because the principal is repaid more quickly, resulting in less interest accruing over time.
