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### Question

Mis Pillay's Cheque Account Balance

1. Explain the term "deposit" according to the given context.
2. Determine Mrs. Pillay's salary that was deposited into her bank account.

- Mrs. Pillay's initial balance: [tex] - R9xot [/tex]
- New balance after deposit: [tex] R8 \, 200 [/tex]
- Calculate the deposited amount.

3. Deposit fee for this type of account:

- Fee: [tex] 5 \times 1.20 \% [/tex] of the value deposited.
- Write down the minimum bank charges for the salary deposited.

4. Mrs. Pillay intends to purchase a birthday present for her mother.

- Table 1 below shows her current plan for two types of interest offered by the bank:

| Number of Years | 0 | 1 | 2 | 3 | 4 |
|-----------------|---|---|---|---|---|
| Investment A | R1 000 | R1 080 | R1 160 | R1 240 | R1 320 |
| Investment B | R1 060 | R1 080 | R1 166.40 | R1 259.71 | R1 360.49 |

- Using the table above, answer the following questions:

4.1 Identify the type of interest used on Investment A and explain your answer.

4.2 Use the investment of R1 000 and the interest rate to show how the amount of R1 259.71 was calculated in Investment B at the end of the 3rd year.



Answer :

GinnyAnswer
### 1.1.1 Explanation of "Deposit" in Context
In this context, a "deposit" refers to the addition of money to Mrs. Pillay’s bank account. Specifically, it is the action of her salary being added to her account, changing her account balance.

### 1.1.2 Determining Mrs. Pillay's Salary
Mrs. Pillay had a previous balance of -R9,600 in her cheque account. After her salary was deposited, the new balance became R8,200. To find out her salary:
[tex]\[ \text{Salary deposited} = \text{New balance} - \text{Old balance} \][/tex]
[tex]\[ \text{Salary deposited} = R8,200 - (-R9,600) = R8,200 + R9,600 = R17,800 \][/tex]

Mrs. Pillay's salary that was deposited into her bank account is R17,800.

### 1.1.3 Minimum Bank Charges for the Salary Deposited
The deposit fee for this type of account is given as R5 plus 1.20% of the value deposited.
[tex]\[ \text{Deposit fee} = R5 + 1.20\% \text{ of } R17,800 \][/tex]
[tex]\[ \text{Deposit fee} = R5 + \left(\frac{1.20}{100} \times R17,800\right) \][/tex]
[tex]\[ \text{Deposit fee} = R5 + R213.60 = R218.60 \][/tex]

The minimum bank charges for depositing the salary is R218.60.

### 2.1 Identify the Type of Interest for Investment A
Investment A increases the same fixed amount each year, so the interest added each year is constant. This is indicative of simple interest. With simple interest, the amount of interest accrued is linear and does not compound over time.

### 2.2 Calculation for Investment B at the End of the 3rd Year
Investment B uses compound interest, where interest is added to the principal, and subsequent interest calculations are based on the increased amount.

Given:
- Principal [tex]\( P = R1,000 \)[/tex]
- Annual interest rate [tex]\( r = 8\% = 0.08 \)[/tex]

The formula for the amount [tex]\( A \)[/tex] after a certain number of years [tex]\( n \)[/tex] under compound interest is:
[tex]\[ A = P (1 + r)^n \][/tex]

For the end of the 3rd year:
[tex]\[ A = 1,000 \left(1 + 0.08\right)^3 \][/tex]
[tex]\[ A = 1,000 \left(1.08\right)^3 \][/tex]
[tex]\[ A = 1,000 \times 1.259712 \][/tex]
[tex]\[ A = R1,259.71 \][/tex]

Thus, the amount of R1,259.71 was calculated by using the compound interest formula at the end of the 3rd year.

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