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Sagot :
Certainly, let's go through the points step by step.
### 1. Difference between an Income-and-Expenditure Statement and a Budget
Income-and-Expenditure Statement:
- Definition: It records actual income received and expenses incurred over a specific period, usually a month.
- Purpose: To analyze past financial activity and understand spending habits.
- Nature: Historical, reflecting what has already happened.
- Example: The total expenses and income documented for the previous month are an income-and-expenditure statement.
Budget:
- Definition: It is a plan for expected income and anticipated expenses for a future period.
- Purpose: To allocate funds in advance and manage spending according to financial goals.
- Nature: Forward-looking, predicting what will happen.
- Example: Planning how to spend the available income in the upcoming month, considering factors like inflation.
### 2. Budget for the Next Month
Given:
- Income = R 200
- Expenses and their monthly inflation-adjusted values (8% per year)
#### Calculation:
Annual Inflation Rate: 0.08
Monthly Inflation Factor:
[tex]\[ (1 + \text{Annual Inflation Rate})^{1/12} \][/tex]
Let's adjust the expenses for the next month including the inflation:
Movies:
[tex]\[ 30.00 \times \text{inflation factor} = 30.193020903300102 \][/tex]
Sweets and Fast Food:
[tex]\[ 76.75 \times \text{inflation factor} = 77.24381181094276 \][/tex]
Cold Drinks:
[tex]\[ 40.10 \times \text{inflation factor} = 40.35800460741114 \][/tex]
Clothes:
[tex]\[ 110.95 \times \text{inflation factor} = 111.66385564070488 \][/tex]
Magazines:
[tex]\[ 54.05 \times \text{inflation factor} = 54.397759327445684 \][/tex]
Transport:
[tex]\[ 18.50 \times \text{inflation factor} = 18.619029557035063 \][/tex]
Sport:
[tex]\[ 20.00 \times \text{inflation factor} = 20.12868060220007 \][/tex]
Gifts:
- Original expense for one gift: R 50.00
- Adjusted for two gifts:
[tex]\[ 2 \times (50.00 \times \text{inflation factor}) = 100.64340301100034 \][/tex]
#### Total Adjusted Expenses:
[tex]\[ 30.193020903300102 + 77.24381181094276 + 40.35800460741114 + 111.66385564070488 + 54.397759327445684 + 18.619029557035063 + 20.12868060220007 + 100.64340301100034 = 453.24756546004005 \][/tex]
### a) Budget for the Next Month:
[tex]\[ \begin{array}{|l|r|} \hline \text{Item} & \text{Expense (R)} \\ \hline \text{Income} & 200.00 \\ \hline \text{Movies} & 30.19 \\ \hline \text{Sweets and Fast Food} & 77.24 \\ \hline \text{Cold Drinks} & 40.36 \\ \hline \text{Clothes} & 111.66 \\ \hline \text{Magazines} & 54.40 \\ \hline \text{Transport} & 18.62 \\ \hline \text{Sport} & 20.13 \\ \hline \text{Gifts (Two)} & 100.64 \\ \hline \text{Total Expenses} & 453.25 \\ \hline \end{array} \][/tex]
### b) Savings Calculation:
[tex]\[ \text{Income - Total Adjusted Expenses} = 200.00 - 453.25 = -253.25 \][/tex]
### Result:
If your income remains the same at R 200, the total expenses for the next month, accounting for inflation and buying two gifts, would be R 453.25. This would result in a deficit (negative savings) of R 253.25 by the end of the next month.
### 1. Difference between an Income-and-Expenditure Statement and a Budget
Income-and-Expenditure Statement:
- Definition: It records actual income received and expenses incurred over a specific period, usually a month.
- Purpose: To analyze past financial activity and understand spending habits.
- Nature: Historical, reflecting what has already happened.
- Example: The total expenses and income documented for the previous month are an income-and-expenditure statement.
Budget:
- Definition: It is a plan for expected income and anticipated expenses for a future period.
- Purpose: To allocate funds in advance and manage spending according to financial goals.
- Nature: Forward-looking, predicting what will happen.
- Example: Planning how to spend the available income in the upcoming month, considering factors like inflation.
### 2. Budget for the Next Month
Given:
- Income = R 200
- Expenses and their monthly inflation-adjusted values (8% per year)
#### Calculation:
Annual Inflation Rate: 0.08
Monthly Inflation Factor:
[tex]\[ (1 + \text{Annual Inflation Rate})^{1/12} \][/tex]
Let's adjust the expenses for the next month including the inflation:
Movies:
[tex]\[ 30.00 \times \text{inflation factor} = 30.193020903300102 \][/tex]
Sweets and Fast Food:
[tex]\[ 76.75 \times \text{inflation factor} = 77.24381181094276 \][/tex]
Cold Drinks:
[tex]\[ 40.10 \times \text{inflation factor} = 40.35800460741114 \][/tex]
Clothes:
[tex]\[ 110.95 \times \text{inflation factor} = 111.66385564070488 \][/tex]
Magazines:
[tex]\[ 54.05 \times \text{inflation factor} = 54.397759327445684 \][/tex]
Transport:
[tex]\[ 18.50 \times \text{inflation factor} = 18.619029557035063 \][/tex]
Sport:
[tex]\[ 20.00 \times \text{inflation factor} = 20.12868060220007 \][/tex]
Gifts:
- Original expense for one gift: R 50.00
- Adjusted for two gifts:
[tex]\[ 2 \times (50.00 \times \text{inflation factor}) = 100.64340301100034 \][/tex]
#### Total Adjusted Expenses:
[tex]\[ 30.193020903300102 + 77.24381181094276 + 40.35800460741114 + 111.66385564070488 + 54.397759327445684 + 18.619029557035063 + 20.12868060220007 + 100.64340301100034 = 453.24756546004005 \][/tex]
### a) Budget for the Next Month:
[tex]\[ \begin{array}{|l|r|} \hline \text{Item} & \text{Expense (R)} \\ \hline \text{Income} & 200.00 \\ \hline \text{Movies} & 30.19 \\ \hline \text{Sweets and Fast Food} & 77.24 \\ \hline \text{Cold Drinks} & 40.36 \\ \hline \text{Clothes} & 111.66 \\ \hline \text{Magazines} & 54.40 \\ \hline \text{Transport} & 18.62 \\ \hline \text{Sport} & 20.13 \\ \hline \text{Gifts (Two)} & 100.64 \\ \hline \text{Total Expenses} & 453.25 \\ \hline \end{array} \][/tex]
### b) Savings Calculation:
[tex]\[ \text{Income - Total Adjusted Expenses} = 200.00 - 453.25 = -253.25 \][/tex]
### Result:
If your income remains the same at R 200, the total expenses for the next month, accounting for inflation and buying two gifts, would be R 453.25. This would result in a deficit (negative savings) of R 253.25 by the end of the next month.
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