Sure! Let's work through this systematically.
### Completing the Table
We need to calculate the values for:
- [tex]\(\Lambda\)[/tex]
- [tex]\(B\)[/tex]
- [tex]\(C\)[/tex]
Given:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
R 15102.76 & R 1386.94 & A & R 2090.57 & R 150397.13 \\
\hline
B & R 1380.49 & R 151979.62 & C & R 149889.12 \\
\hline
\end{tabular}
\][/tex]
1. Calculation of [tex]\(\Lambda\)[/tex]:
[tex]\[
\Lambda = R15102.76 + R1386.94 + R1380.49
\][/tex]
[tex]\[
\Lambda = 15102.76 + 1386.94 + 1380.49 = 17870.19
\][/tex]
2. Calculation of [tex]\(B\)[/tex]:
[tex]\[
B = R151979.62 - R1386.94 - R2090.57
\][/tex]
[tex]\[
B = 151979.62 - 1386.94 - 2090.57 = 148502.11
\][/tex]
3. Calculation of [tex]\(C\)[/tex]:
[tex]\[
C = R151979.62 + R149889.12 - 2 \times R15102.76
\][/tex]
[tex]\[
C = 151979.62 + 149889.12 - 2 \times 15102.76 = 271663.22
\][/tex]
So, the completed table is:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
R 15102.76 & R 1386.94 & 17870.19 & R 2090.57 & R 150397.13 \\
\hline
148502.11 & R 1380.49 & R 151979.62 & 271663.22 & R 149889.12 \\
\hline
\end{tabular}
\][/tex]
### Describing the Graph Shape
Assuming the values represent some sort of time series data over a 72-month period, such as mortgage repayment details:
- The shape of the graph showing the remaining mortgage balance over time would typically start high and gradually decrease.
- This is because each month, mortgage payments reduce the balance. The largest portion of the interest is paid off early, and more principal is paid off in later months.
### Bond Calculation for Mrs. Mkhize
Given:
- Property price: [tex]\(R 2,440,000\)[/tex]
- Deposit percentage: [tex]\(25\%\)[/tex]
4. Deposit Value:
[tex]\[
\text{Deposit Value} = \text{Property Price} \times \text{Deposit Percentage}
\][/tex]
[tex]\[
\text{Deposit Value} = 2,440,000 \times 0.25 = 610,000
\][/tex]
5. Balance Loan:
[tex]\[
\text{Loan Balance} = \text{Property Price} - \text{Deposit Value}
\][/tex]
[tex]\[
\text{Loan Balance} = 2,440,000 - 610,000 = 1,830,000
\][/tex]
So, the deposit value is [tex]\(R 610,000\)[/tex] and the loan balance is [tex]\(R 1,830,000\)[/tex].
To summarize, we have:
- Completed table values: [tex]\(\Lambda = 17870.19\)[/tex], [tex]\(B = 148502.11\)[/tex], [tex]\(C = 271663.22\)[/tex]
- The graph shape is generally a decreasing curve for mortgage balances.
- Mrs. Mkhize's deposit value is [tex]\(R 610,000\)[/tex] and the remaining loan balance is [tex]\(R 1,830,000\)[/tex].
