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1. Explain the difference between an income-and-expenditure statement and a budget.

2. You wrote down your income and expenses for one month:

\begin{tabular}{|l|l|r|}
\hline Income: & \begin{tabular}{l}
Pocket money \\
Working on Saturdays at a florist
\end{tabular} & R 200 \\
\hline Expenses: & Movies & [tex]$R 30,00$[/tex] \\
\hline & Sweets and fast food & [tex]$R 76,75$[/tex] \\
\hline & Cold drinks & [tex]$R 40,10$[/tex] \\
\hline & Clothes & [tex]$R 110,95$[/tex] \\
\hline & Magazines & [tex]$R 54,05$[/tex] \\
\hline & Transport & [tex]$R 18,50$[/tex] \\
\hline & Sport & [tex]$R 20,00$[/tex] \\
\hline & Gifts (one) & [tex]$R 50,00$[/tex] \\
\hline
\end{tabular}

a) Use this information to draw up a budget for the next month. Take into account that the inflation rate is [tex]$8 \%$[/tex] per year. You will also have to buy two gifts instead of one.

b) If your income remains the same, determine how much you will be able to save at the end of the next month.



Answer :

GinnyAnswer
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.