ngazibinidalasile220
Answered

Jonella has a Pegasus Bank savings account which offers [tex]1.35 \%[/tex] p.a. on all credit balances. Her transactions for the month of May are summarized in the table below.

\begin{tabular}{|l|l|l|l|}
\hline
Date & Description & Amount & Balance \\
\hline
01/05 & Opening balance & & 10,000.00 \\
\hline
01/05 & ATM cash deposit & 2,000.00 & 12,000.00 \\
\hline
01/05 & Transaction fee & & \\
\hline
02/05 & ATM withdrawal (own bank) & -1,000.00 & \\
\hline
02/05 & Transaction fee & & \\
\hline
07/05 & Cash branch withdrawal & -1,880.00 & \\
\hline
07/05 & Bank fees & -45.00 & \\
\hline
23/05 & Electronic transfer & 2,800.00 & 11,850.00 \\
\hline
23/05 & Bank fees & & 7,850.00 \\
\hline
\end{tabular}

\begin{tabular}{|l|l|}
\hline
\multicolumn{2}{|l|}{Transaction/banking fees schedule} \\
\hline
Savings account: & \\
\hline
ATM deposit and electronic transfers: & Free \\
Own ATM withdrawal: & R3.35 plus R0.95 per R100 or part thereof \\
Other bank ATM withdrawal: & R8.75 plus R0.95 per R100 or part thereof \\
Branch withdrawal: & R20.00 plus R1.10 per R100 or part thereof \\
\hline
\end{tabular}

a. Use the table of banking fees to calculate and fill in all the bank charges for this statement.

b. Use the details given to complete the balance column for this account.

(4)

(4)

c. Calculate the daily interest rate, correct to six decimal places. Explain why it is necessary to use six decimal places.



Answer :

GinnyAnswer
Let's solve the problem step-by-step:

### Part (a): Calculate and fill in all the bank charges for this statement.

1. Opening Balance on 01/05:
- Opening balance is R10000.00.

2. ATM Cash Deposit on 01/05:
- Amount deposited: R2000.00
- There is no transaction fee for ATM deposits.

3. ATM Withdrawal on 02/05:
- Amount withdrawn: -R1000.00
- Fee structure: R3.35 + (R0.95 per R100 or part thereof)
- Calculation of fee: [tex]\( R3.35 + R0.95 \times \lceil \frac{1000}{100} \rceil = R3.35 + R0.95 \times 10 = R3.35 + R9.50 = R12.85 \)[/tex]
- So, the transaction fee for the ATM withdrawal on 02/05 is R12.85.

4. Branch Withdrawal on 07/05:
- Amount withdrawn: -R1880.00
- Fee structure: R20.00 + (R1.10 per R100 or part thereof)
- Calculation of fee: [tex]\( R20.00 + R1.10 \times \lceil \frac{1880}{100} \rceil = R20.00 + R1.10 \times 19 = R20.00 + R20.90 = R40.90 \)[/tex]
- So, the transaction fee for the branch withdrawal on 07/05 is R40.90.

5. Bank Fees on 07/05:
- Bank fees incurred: R45.00

6. Electronic Transfer on 23/05:
- Amount transferred: R2800.00
- There is no transaction fee for electronic transfers.

7. Bank Fees on 23/05:
- Bank fees incurred: R7850.00

### Part (b): Complete the balance column for this account.

Now we update the balance after each transaction:

1. Opening Balance on 01/05:
- Balance: R10000.00

2. Balance after ATM Cash Deposit on 01/05:
- New Balance: [tex]\( R10000.00 + R2000.00 = R12000.00 \)[/tex]

3. Balance after ATM Withdrawal and Fee on 02/05:
- New Balance: [tex]\( R12000.00 - R1000.00 - R12.85 = R10987.15 \)[/tex]

4. Balance after Cash Branch Withdrawal, Fee, and Bank Fees on 07/05:
- New Balance: [tex]\( R10987.15 - R1880.00 - R40.90 - R45.00 = R9021.25 \)[/tex]

5. Balance after Electronic Transfer and Bank Fees on 23/05:
- New Balance: [tex]\( R9021.25 + R2800.00 + R7850.00 = R19671.25 \)[/tex]

Here is the updated table:

| Date | Description | Amount | Balance |
|----------|---------------------------|---------|--------------|
| 01/05 | Opening balance | | R10000.00 |
| 01/05 | ATM cash deposit | R2000.00| R12000.00 |
| 02/05 | ATM withdrawal (own bank) | -R1000.00| |
| 02/05 | Transaction fee | -R12.85 | R10987.15 |
| 07/05 | Cash branch withdrawal | -R1880.00| |
| 07/05 | Transaction fee | -R40.90 | |
| 07/05 | Bank fees | -R45.00 | R9021.25 |
| 23/05 | Electronic transfer | R2800.00| R9021.25 |
| 23/05 | Bank fees | R7850.00| R19671.25 |

### Part (c): Calculate the daily interest rate, correct to six decimal places.

Given the annual interest rate of 1.35%, we need to convert this to a daily interest rate:

1. Annual Interest Rate: 0.0135 (1.35% as a decimal)

2. Daily Interest Rate Formula:
[tex]\[ \text{Daily Interest Rate} = \left(1 + \text{Annual Interest Rate}\right)^{\frac{1}{365}} - 1 \][/tex]

3. Calculation:
[tex]\[ \text{Daily Interest Rate} = \left(1 + 0.0135\right)^{\frac{1}{365}} - 1 \approx 0.000037 \][/tex]

The daily interest rate, correct to six decimal places, is [tex]\(0.000037\)[/tex].

It is necessary to use six decimal places for the daily interest rate because the interest rates are typically very small, and more precision is required to ensure accurate calculations over time. Small differences can compound significantly over long periods.