Ball Hamilton
11/10/2023 · Senior High School
Find simple interest and total amount of ₹ 8250 at the rate 0 \( 16 \% \) per annum for \( 3 \frac{1}{2} \) years.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To calculate the simple interest (SI) and the total amount (A) for a principal amount (P) of ₹ 8250 at an interest rate (R) of 16% per annum for a time period (T) of \( 3 \frac{1}{2} \) years, we can use the following formulas:
1. **Simple Interest (SI)**:
\[
SI = \frac{P \times R \times T}{100}
\]
2. **Total Amount (A)**:
\[
A = P + SI
\]
### Step 1: Convert the time period
First, convert \( 3 \frac{1}{2} \) years into a decimal:
\[
3 \frac{1}{2} = 3 + \frac{1}{2} = 3 + 0.5 = 3.5 \text{ years}
\]
### Step 2: Calculate Simple Interest
Now, substitute the values into the SI formula:
- \( P = 8250 \)
- \( R = 16 \)
- \( T = 3.5 \)
\[
SI = \frac{8250 \times 16 \times 3.5}{100}
\]
Calculating the multiplication:
\[
8250 \times 16 = 132000
\]
\[
132000 \times 3.5 = 462000
\]
Now, divide by 100:
\[
SI = \frac{462000}{100} = 4620
\]
### Step 3: Calculate Total Amount
Now, calculate the total amount:
\[
A = P + SI = 8250 + 4620 = 12870
\]
### Final Results
- **Simple Interest (SI)**: ₹ 4620
- **Total Amount (A)**: ₹ 12870
Thus, the simple interest is ₹ 4620 and the total amount is ₹ 12870.
Quick Answer
Simple interest is ₹ 4620 and total amount is ₹ 12870.
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