Sure, let's solve this problem step-by-step using the given values.
### Step 1: Identify the given values
- Principal amount (P): [tex]$24,000
- Annual interest rate (r): 12% or 0.12
- Date borrowed: May 04, 2023
- Date repaid: July 09, 2023
### Step 2: Calculate the time period
The time period between the borrowing date and the repayment date needs to be calculated in days.
Given:
- Borrowed on May 04, 2023
- Repaid on July 09, 2023
To find the number of days between the two dates, we simply calculate:
- Days in May after May 4: 27 days (from May 5 to May 31)
- Days in June: 30 days
- Days in July up to July 9: 9 days
Summing these up:
27 (May) + 30 (June) + 9 (July) = 66 days
### Step 3: Calculate the simple interest
The formula for simple interest (SI) is given by:
\[ \text{SI} = \frac{P \times r \times T}{360} \]
where \( P \) is the principal amount, \( r \) is the annual interest rate, and \( T \) is the time period in days (using a 360-day year convention).
Plugging in the values:
\[ \text{SI} = \frac{24,000 \times 0.12 \times 66}{360} \]
\[ \text{SI} = \frac{24,000 \times 7.92}{360} \]
\[ \text{SI} = 528 \]
So, the simple interest for the time period is $[/tex]528.
### Step 4: Calculate the amount to be paid back
The total amount to be paid back is the sum of the principal and the simple interest.
[tex]\[ \text{Total Amount} = P + \text{SI} \][/tex]
[tex]\[ \text{Total Amount} = 24,000 + 528 \][/tex]
[tex]\[ \text{Total Amount} = 24,528 \][/tex]
### Summary
- Time (T): 66 days
- Simple Interest (SI): [tex]$528.00
- Amount Paid Back: $[/tex]24,528.00
So, the completed table will look like this:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& & Interest Rate & Date Borrowed & Date Repaid & Time & Simple Interest & Amount Paid Back \\
\hline
\$ & 24,000 & 12\% & May 04 & Jul 09 & 66 days & \$528.00 & \$24,528.00 \\
\hline
\end{tabular}
\][/tex]
