Answer :
To approach these problems, we'll go step-by-step through each part.
### Part (a) Calculate the PAYE Income Tax that Tyler owes each month.
Firstly, let's consider Tyler’s taxable income. Tyler's taxable income includes his salary and the taxable portion of his travel allowance.
#### Gross salary and taxable travel allowance:
- Monthly salary: R 12,000
- Travel allowance: R 2,000
Therefore, the monthly taxable income is:
[tex]\[ \text{Monthly Taxable Income} = 12,000 + 2,000 = 14,000 \][/tex]
To determine the yearly taxable income, multiply the monthly taxable income by 12:
[tex]\[ \text{Yearly Taxable Income} = 14,000 \times 12 = 168,000 \][/tex]
Using the tax brackets provided:
- For annual income up to R 165,600: 18% of each R 1
[tex]\[ \text{Annual Tax} = 165,600 \times 0.18 = 29,808 \][/tex]
For the remaining income above R 165,600 and up to R 258,750:
[tex]\[ \text{Taxable Income above R 165,600} = 168,000 - 165,600 = 2,400 \][/tex]
[tex]\[ \text{Tax on this portion} = 2,400 \times 0.25 = 600 \][/tex]
So, the total annual tax would therefore be:
[tex]\[ \text{Total Annual Tax} = 29,808 + 600 = 30,408 \][/tex]
Subtract the primary rebate (R 12,080):
[tex]\[ \text{Annual Tax after rebate} = 30,408 - 12,080 = 18,328 \][/tex]
Finally, to find the monthly PAYE Income Tax:
[tex]\[ \text{Monthly PAYE Tax} = \frac{18,328}{12} \approx 1527.33 \][/tex]
Therefore, the monthly PAYE Income Tax Tyler owes is about [tex]\( \approx R 1527.33 \)[/tex].
### Part (b) Calculate Tyler's Net Income per month.
To find Tyler's net income, we subtract all monthly deductions from the total earnings.
Here's what Tyler’s deductions look like:
- Monthly PAYE Income Tax: [tex]\( R ~1527.33 \)[/tex]
- Bond repayment to the bank: [tex]\( R ~1200 \)[/tex]
- Retirement Fund payment: [tex]\( R ~612 \)[/tex]
- Unemployment Insurance Fund payment: [tex]\( R ~120 \)[/tex]
- Life Insurance payment: [tex]\( R ~600 \)[/tex]
Adding up all the deductions:
[tex]\[ \text{Total Deductions} = 1527.33 + 1200 + 612 + 120 + 600 = 4059.33 \][/tex]
Subtracting these from the total earnings:
[tex]\[ \text{Net Income} = 15,132 - 4059.33 \approx 11,072.67 \][/tex]
So, Tyler’s Net Income per month is about [tex]\( \approx R 11,072.67 \)[/tex].
### Part (c) Calculate the total amount that Tyler will pay for his flat if he pays it off over 15 years.
Tyler repays a fixed amount for the first 6 years and then an increased amount for the remaining 9 years.
#### First 6 years:
Monthly bond repayment: [tex]\( R 1200 \)[/tex]
[tex]\[ \text{Total Repayment for 6 years} = 1200 \times 12 \times 6 = 86,400 \][/tex]
#### After 6 years, repayments increase by 12%:
[tex]\[ \text{New Monthly Repayment} = 1200 \times 1.12 = 1344 \][/tex]
[tex]\[ \text{Total Repayment for 9 years} = 1344 \times 12 \times 9 = 145,152 \][/tex]
Adding both periods together:
[tex]\[ \text{Total Amount Paid for the Flat} = 86,400 + 145,152 = 231,552 \][/tex]
Thus, Tyler will pay a total of [tex]\( R 231,552 \)[/tex] for his flat.
### Part (d) Calculate the price of the flat that Tyler bought if he is charged 8% simple interest for 15 years.
Given the formula for the future value: [tex]\( F V = P V (1 + i \times n) \)[/tex]
Where:
- [tex]\( F V \)[/tex] is future value (the total bond payment Tyler made)
- [tex]\( i \)[/tex] is the interest rate (0.08)
- [tex]\( n \)[/tex] is the number of years (15)
We solve for [tex]\( P V \)[/tex] (the price of the flat):
[tex]\[ 231,552 = P V (1 + 0.08 \times 15) \][/tex]
[tex]\[ 231,552 = P V (1 + 1.2) \][/tex]
[tex]\[ 231,552 = P V \times 2.2 \][/tex]
[tex]\[ P V = \frac{231,552}{2.2} = 105,250.91 \][/tex]
The price of the flat that Tyler bought is approximately [tex]\( R 105,250.91 \)[/tex].
### Part (a) Calculate the PAYE Income Tax that Tyler owes each month.
Firstly, let's consider Tyler’s taxable income. Tyler's taxable income includes his salary and the taxable portion of his travel allowance.
#### Gross salary and taxable travel allowance:
- Monthly salary: R 12,000
- Travel allowance: R 2,000
Therefore, the monthly taxable income is:
[tex]\[ \text{Monthly Taxable Income} = 12,000 + 2,000 = 14,000 \][/tex]
To determine the yearly taxable income, multiply the monthly taxable income by 12:
[tex]\[ \text{Yearly Taxable Income} = 14,000 \times 12 = 168,000 \][/tex]
Using the tax brackets provided:
- For annual income up to R 165,600: 18% of each R 1
[tex]\[ \text{Annual Tax} = 165,600 \times 0.18 = 29,808 \][/tex]
For the remaining income above R 165,600 and up to R 258,750:
[tex]\[ \text{Taxable Income above R 165,600} = 168,000 - 165,600 = 2,400 \][/tex]
[tex]\[ \text{Tax on this portion} = 2,400 \times 0.25 = 600 \][/tex]
So, the total annual tax would therefore be:
[tex]\[ \text{Total Annual Tax} = 29,808 + 600 = 30,408 \][/tex]
Subtract the primary rebate (R 12,080):
[tex]\[ \text{Annual Tax after rebate} = 30,408 - 12,080 = 18,328 \][/tex]
Finally, to find the monthly PAYE Income Tax:
[tex]\[ \text{Monthly PAYE Tax} = \frac{18,328}{12} \approx 1527.33 \][/tex]
Therefore, the monthly PAYE Income Tax Tyler owes is about [tex]\( \approx R 1527.33 \)[/tex].
### Part (b) Calculate Tyler's Net Income per month.
To find Tyler's net income, we subtract all monthly deductions from the total earnings.
Here's what Tyler’s deductions look like:
- Monthly PAYE Income Tax: [tex]\( R ~1527.33 \)[/tex]
- Bond repayment to the bank: [tex]\( R ~1200 \)[/tex]
- Retirement Fund payment: [tex]\( R ~612 \)[/tex]
- Unemployment Insurance Fund payment: [tex]\( R ~120 \)[/tex]
- Life Insurance payment: [tex]\( R ~600 \)[/tex]
Adding up all the deductions:
[tex]\[ \text{Total Deductions} = 1527.33 + 1200 + 612 + 120 + 600 = 4059.33 \][/tex]
Subtracting these from the total earnings:
[tex]\[ \text{Net Income} = 15,132 - 4059.33 \approx 11,072.67 \][/tex]
So, Tyler’s Net Income per month is about [tex]\( \approx R 11,072.67 \)[/tex].
### Part (c) Calculate the total amount that Tyler will pay for his flat if he pays it off over 15 years.
Tyler repays a fixed amount for the first 6 years and then an increased amount for the remaining 9 years.
#### First 6 years:
Monthly bond repayment: [tex]\( R 1200 \)[/tex]
[tex]\[ \text{Total Repayment for 6 years} = 1200 \times 12 \times 6 = 86,400 \][/tex]
#### After 6 years, repayments increase by 12%:
[tex]\[ \text{New Monthly Repayment} = 1200 \times 1.12 = 1344 \][/tex]
[tex]\[ \text{Total Repayment for 9 years} = 1344 \times 12 \times 9 = 145,152 \][/tex]
Adding both periods together:
[tex]\[ \text{Total Amount Paid for the Flat} = 86,400 + 145,152 = 231,552 \][/tex]
Thus, Tyler will pay a total of [tex]\( R 231,552 \)[/tex] for his flat.
### Part (d) Calculate the price of the flat that Tyler bought if he is charged 8% simple interest for 15 years.
Given the formula for the future value: [tex]\( F V = P V (1 + i \times n) \)[/tex]
Where:
- [tex]\( F V \)[/tex] is future value (the total bond payment Tyler made)
- [tex]\( i \)[/tex] is the interest rate (0.08)
- [tex]\( n \)[/tex] is the number of years (15)
We solve for [tex]\( P V \)[/tex] (the price of the flat):
[tex]\[ 231,552 = P V (1 + 0.08 \times 15) \][/tex]
[tex]\[ 231,552 = P V (1 + 1.2) \][/tex]
[tex]\[ 231,552 = P V \times 2.2 \][/tex]
[tex]\[ P V = \frac{231,552}{2.2} = 105,250.91 \][/tex]
The price of the flat that Tyler bought is approximately [tex]\( R 105,250.91 \)[/tex].
