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Sure, let's break down the questions and solve them step-by-step.
### 3.1.1 Calculate the total amount deposited during the month of October.
The transactions are as follows:
- 2 cash deposits of R16500.00 each at their local branch
- 1 cash deposit of R4500.00 at ATM
- 2 cheque deposits of R20000.00 each
To find out the total amount deposited:
- Cash deposit at Branch 1: R16500.00
- Cash deposit at Branch 2: R16500.00
- Cash deposit at ATM: R4500.00
- Cheque deposit 1: R20000.00
- Cheque deposit 2: R20000.00
Adding these amounts:
[tex]\[ \text{Total deposit} = R16500 + R16500 + R4500 + R20000 + R20000 = R77500 \][/tex]
So, the total amount deposited during October is R77500.
### 3.1.2 Calculate the bank charges on the R4500.00 deposit at the ATM.
The ATM deposit fee is R1.70 per R100 (or part thereof).
Breaking down the deposit amount for R4500:
- Each R100 incurs a fee of R1.70.
- R4500 means we have 45 full groups of R100.
Thus, we calculate:
[tex]\[ \text{ATM fee} = \left\lceil \frac{4500}{100} \right\rceil \times 1.70 = 45 \times 1.70 = R76.5 \][/tex]
Therefore, the bank charges on the R4500.00 deposit at the ATM are R76.50.
### 3.1.3 Mention ONE advantage of using an ATM.
An example advantage of using an ATM is: Convenience, as ATMs are available 24/7 and can be used at any time.
### 3.2.1 Bank A offers 7.3% p.a. simple interest for 2 years. Calculate the interest earned over the 2 years.
The formula for simple interest is:
[tex]\[ \text{Simple Interest} = P \times R \times T \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount (R410.00)
- [tex]\( R \)[/tex] is the annual interest rate (7.3% or 0.073)
- [tex]\( T \)[/tex] is the time period in years (2 years)
Plugging in the values:
[tex]\[ \text{Simple Interest} = 410 \times 0.073 \times 2 = R59.86 \][/tex]
So, the interest earned from Bank A over the 2 years is R59.86.
### 3.2.2 Bank B offers 6.9% p.a. interest compounded annually for 2 years. Calculate the interest earned over the 2 years.
The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount (R410.00)
- [tex]\( R \)[/tex] is the annual interest rate (6.9% or 0.069)
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year (1, since it's compounded annually)
- [tex]\( T \)[/tex] is the time period in years (2 years)
First, calculate the amount [tex]\( A \)[/tex]:
[tex]\[ A = 410 \left(1 + \frac{0.069}{1}\right)^{1 \times 2} = 410 \left(1 + 0.069\right)^2 = 410 \left(1.069\right)^2 \][/tex]
[tex]\[ A = 410 \times 1.1420441 \approx 468.53201 \][/tex]
The compound interest earned is:
[tex]\[ \text{Compound Interest} = A - P = 468.53201 - 410 = R58.53201 \][/tex]
Therefore, the interest earned from Bank B over the 2 years is R58.53.
### Summary:
- Total amount deposited during October: R77500
- Bank charges on the R4500.00 deposit at the ATM: R76.50
- Advantage of using an ATM: Convenience, as ATMs are available 24/7 and can be used at any time.
- Interest earned from Bank A (simple interest): R59.86
- Interest earned from Bank B (compound interest): R58.53
### 3.1.1 Calculate the total amount deposited during the month of October.
The transactions are as follows:
- 2 cash deposits of R16500.00 each at their local branch
- 1 cash deposit of R4500.00 at ATM
- 2 cheque deposits of R20000.00 each
To find out the total amount deposited:
- Cash deposit at Branch 1: R16500.00
- Cash deposit at Branch 2: R16500.00
- Cash deposit at ATM: R4500.00
- Cheque deposit 1: R20000.00
- Cheque deposit 2: R20000.00
Adding these amounts:
[tex]\[ \text{Total deposit} = R16500 + R16500 + R4500 + R20000 + R20000 = R77500 \][/tex]
So, the total amount deposited during October is R77500.
### 3.1.2 Calculate the bank charges on the R4500.00 deposit at the ATM.
The ATM deposit fee is R1.70 per R100 (or part thereof).
Breaking down the deposit amount for R4500:
- Each R100 incurs a fee of R1.70.
- R4500 means we have 45 full groups of R100.
Thus, we calculate:
[tex]\[ \text{ATM fee} = \left\lceil \frac{4500}{100} \right\rceil \times 1.70 = 45 \times 1.70 = R76.5 \][/tex]
Therefore, the bank charges on the R4500.00 deposit at the ATM are R76.50.
### 3.1.3 Mention ONE advantage of using an ATM.
An example advantage of using an ATM is: Convenience, as ATMs are available 24/7 and can be used at any time.
### 3.2.1 Bank A offers 7.3% p.a. simple interest for 2 years. Calculate the interest earned over the 2 years.
The formula for simple interest is:
[tex]\[ \text{Simple Interest} = P \times R \times T \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount (R410.00)
- [tex]\( R \)[/tex] is the annual interest rate (7.3% or 0.073)
- [tex]\( T \)[/tex] is the time period in years (2 years)
Plugging in the values:
[tex]\[ \text{Simple Interest} = 410 \times 0.073 \times 2 = R59.86 \][/tex]
So, the interest earned from Bank A over the 2 years is R59.86.
### 3.2.2 Bank B offers 6.9% p.a. interest compounded annually for 2 years. Calculate the interest earned over the 2 years.
The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \][/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount (R410.00)
- [tex]\( R \)[/tex] is the annual interest rate (6.9% or 0.069)
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year (1, since it's compounded annually)
- [tex]\( T \)[/tex] is the time period in years (2 years)
First, calculate the amount [tex]\( A \)[/tex]:
[tex]\[ A = 410 \left(1 + \frac{0.069}{1}\right)^{1 \times 2} = 410 \left(1 + 0.069\right)^2 = 410 \left(1.069\right)^2 \][/tex]
[tex]\[ A = 410 \times 1.1420441 \approx 468.53201 \][/tex]
The compound interest earned is:
[tex]\[ \text{Compound Interest} = A - P = 468.53201 - 410 = R58.53201 \][/tex]
Therefore, the interest earned from Bank B over the 2 years is R58.53.
### Summary:
- Total amount deposited during October: R77500
- Bank charges on the R4500.00 deposit at the ATM: R76.50
- Advantage of using an ATM: Convenience, as ATMs are available 24/7 and can be used at any time.
- Interest earned from Bank A (simple interest): R59.86
- Interest earned from Bank B (compound interest): R58.53
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