Sure, let's complete the table step-by-step with the given information:
1. Principal: [tex]$2,800
2. Interest rate: 7%
3. Date borrowed: March 9
4. Date repaid: June 12
5. Exact time: We need to calculate the exact number of days between March 9 and June 12.
- First, we determine the number of days remaining in March after the 9th:
- March: 31 days total - 9 days passed = 22 days remaining in March.
- Days in the full months after March and before June:
- April: 30 days
- May: 31 days
- Days in June up to the 12th:
- June: 12 days
- Therefore, the exact time is:
\( 22 \text{ (days in March)} + 30 \text{ (days in April)} + 31 \text{ (days in May)} + 12 \text{ (days in June)} = 95 \text{ days} \).
So, the exact time is 95 days.
6. Interest: Next, we calculate the interest using the ordinary interest method.
- Formula: \( \text{Interest} = \text{Principal} \times \text{Interest Rate} \times \frac{\text{Exact Time}}{365} \)
- Plug in the values:
\( \text{Interest} = 2800 \times 0.07 \times \frac{95}{365} \)
- Using precise calculations:
\( \text{Interest} \approx 2800 \times 0.07 \times 0.26027 \approx 51.01 \)
The interest, rounded to the nearest cent, is $[/tex]51.01.
7. Maturity value: This is the sum of the principal and the interest.
- Formula: [tex]\( \text{Maturity Value} = \text{Principal} + \text{Interest} \)[/tex]
- Calculation:
[tex]\( \text{Maturity Value} = 2800 + 51.01 \)[/tex]
[tex]\( \text{Maturity Value} = 2851.01 \)[/tex]
The maturity value, rounded to the nearest cent, is [tex]$2,851.01.
So, the completed table is:
\[
\begin{tabular}{|l|l|c|c|c|c|c|}
\hline
Principal & Interest rate & Date borrowed & Date repaid & Exact time & Interest & Maturity value \\
\hline
\$[/tex] 2,800 & 7\% & Mar. 09 & June 12 & 95 & \[tex]$ 51.01 & \$[/tex] 2,851.01 \\
\hline
\end{tabular}
\]
