### 3.1 Transaction Details for Sekhukhune College
#### 3.1.1 Calculate the Total Amount Deposited in October
The college made the following deposits during October:
1. Two cash deposits of R16,500.00 each at their local branch.
2. One cash deposit of R4,500.00 at an ATM.
3. Two cheque deposits of R20,000.00 each.
Let's add these amounts together to find the total amount deposited:
- Cash deposit at Branch 1: R16,500.00
- Cash deposit at Branch 2: R16,500.00
- Cash deposit at ATM: R4,500.00
- Cheque deposit 1: R20,000.00
- Cheque deposit 2: R20,000.00
Total deposited amount:
[tex]\[ R16,500.00 + R16,500.00 + R4,500.00 + R20,000.00 + R20,000.00 = R77,500.00 \][/tex]
So, the total amount deposited during the month of October is:
[tex]\[
\boxed{R77,500.00}
\][/tex]
#### 3.1.2 Calculate the Bank Charges on the R4,500.00 Deposit at the ATM
The bank charges R1.70 per R100 (or part thereof) for cash deposits at the ATM. To calculate the charges for a R4,500.00 deposit:
First, determine how many R100 units are in R4,500.00:
[tex]\[ \text{Units of R100} = \frac{4500}{100} = 45 \][/tex]
Since the bank charges R1.70 per unit of R100:
[tex]\[ \text{Bank charges} = 45 \times 1.70 = R76.50 \][/tex]
So, the bank charges on the R4,500.00 deposit at the ATM amount to:
[tex]\[
\boxed{R76.50}
\][/tex]
#### 3.1.3 Mention ONE Advantage of Using an ATM
One advantage of using an ATM is that ATM transactions are generally quicker and more convenient as they are available 24/7.
[tex]\[
\boxed{\text{ATM transactions are generally quicker and more convenient as they are available 24/7.}}
\][/tex]
### 3.2 Investment Decision with Bank A and Bank B
#### 3.2.1 Calculate the Interest Earned with Bank A (Simple Interest)
Bank A offers a 7.3% per annum simple interest rate for 2 years. Calculate the interest earned over the 2 years.
Given:
- Principal amount (P) = R5,410.00
- Interest rate (r) = 7.3% = 0.073
- Time period (t) = 2 years
The formula for simple interest (SI) is:
[tex]\[ SI = P \times r \times t \][/tex]
Substitute in the values:
[tex]\[ SI = 5410.00 \times 0.073 \times 2 = R789.86 \][/tex]
So, the interest earned over 2 years with Bank A is:
[tex]\[
\boxed{R789.86}
\][/tex]
#### 3.2.2 Calculate the Interest Earned with Bank B (Compound Interest)
Bank B offers a 6.9% per annum interest rate, compounded annually for 2 years. Calculate the interest earned over the 2 years.
Given:
- Principal amount (P) = R5,410.00
- Interest rate (r) = 6.9% = 0.069
- Time period (t) = 2 years
The formula for compound interest is:
[tex]\[ A = P \left(1 + r \right)^t \][/tex]
where [tex]\( A \)[/tex] is the amount after t years.
Substitute in the values:
[tex]\[ A = 5410.00 \left(1 + 0.069\right)^2 \][/tex]
First, calculate [tex]\( \left(1 + 0.069\right)^2 \)[/tex]:
[tex]\[ \left(1.069\right)^2 = 1.142761 \][/tex]
Now, multiply by the principal amount:
[tex]\[ A = 5410.00 \times 1.142761 = R6,182.34 \][/tex]
The interest earned is:
[tex]\[ \text{Interest} = A - P = R6,182.34 - R5,410.00 = R772.34 \][/tex]
So, the interest earned over 2 years with Bank B is:
[tex]\[
\boxed{R772.34}
\][/tex]
