Responder
The investment resulted in a loss of approximately 132%.
Solución
To find the simple interest rate equivalent to the investment, we can use the formula for simple interest:
\[
I = P \cdot r \cdot t
\]
Where:
- \( I \) is the interest earned,
- \( P \) is the principal amount (initial investment),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.
First, we need to calculate the interest earned \( I \):
\[
I = \text{Final Amount} - \text{Principal} = 5243 - 8000
\]
Next, we convert the time from days to years. Since there are 365 days in a year:
\[
t = \frac{95}{365}
\]
Now we can rearrange the simple interest formula to solve for \( r \):
\[
r = \frac{I}{P \cdot t}
\]
Let's calculate \( I \), \( t \), and then \( r \).
1. Calculate \( I \):
\[
I = 5243 - 8000
\]
2. Calculate \( t \):
\[
t = \frac{95}{365}
\]
3. Finally, calculate \( r \):
\[
r = \frac{I}{8000 \cdot t}
\]
Now, let's perform these calculations step by step.
First, calculate \( I \) and \( t \).
Calculate the value by following steps:
- step0: Calculate:
\(5243-8000\)
- step1: Subtract the numbers:
\(-2757\)
Calculate or simplify the expression \( 95 / 365 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{95}{365}\)
- step1: Reduce the fraction:
\(\frac{19}{73}\)
1. The interest earned \( I \) is:
\[
I = 5243 - 8000 = -2757
\]
2. The time \( t \) in years is:
\[
t = \frac{95}{365} \approx 0.2603 \text{ years}
\]
Now, we can calculate the interest rate \( r \) using the formula:
\[
r = \frac{I}{P \cdot t}
\]
Substituting the values we have:
\[
r = \frac{-2757}{8000 \cdot 0.2603}
\]
Let's calculate \( r \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{-2757}{\left(8000\left(\frac{95}{365}\right)\right)}\)
- step1: Remove the parentheses:
\(\frac{-2757}{8000\left(\frac{95}{365}\right)}\)
- step2: Reduce the fraction:
\(\frac{-2757}{8000\times \frac{19}{73}}\)
- step3: Multiply the numbers:
\(\frac{-2757}{\frac{152000}{73}}\)
- step4: Multiply by the reciprocal:
\(-2757\times \frac{73}{152000}\)
- step5: Multiply:
\(-\frac{2757\times 73}{152000}\)
- step6: Multiply:
\(-\frac{201261}{152000}\)
The interest rate \( r \) is calculated as:
\[
r = -\frac{201261}{152000} \approx -1.32
\]
To express this as a percentage, we multiply by 100:
\[
r \approx -132\%
\]
This indicates a loss rather than a gain, meaning the investment resulted in a negative return. Therefore, the equivalent simple interest rate is approximately \(-132\%\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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