If CI on 25500 for 3 years is 8440.50 then find the rate of interest?

Options

A. `10.5%`
B. `9%`
C. `9.5%`
D. `10%`

Answer

To find the rate of interest when the compound interest (CI) on a principal amount of ₹25,500 for 3 years is ₹8,440.50, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values:**
- Principal (P) = ₹25,500
- Compound Interest (CI) = ₹8,440.50
- Time (T) = 3 years

2. **Calculate the Total Amount (A):**
The total amount (A) after 3 years can be calculated using the formula:
\[ A = P + CI \]
Substituting the values:
\[ A = 25,500 + 8,440.50 = 33,940.50 \]

3. **Set Up the Formula for Compound Interest:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]
Where:
- \( r \) is the rate of interest.
- \( T \) is the time in years.

4. **Substitute the Known Values into the Formula:**
\[ 33,940.50 = 25,500 \left(1 + \frac{r}{100}\right)^3 \]

5. **Divide Both Sides by the Principal (P):**
\[ \frac{33,940.50}{25,500} = \left(1 + \frac{r}{100}\right)^3 \]
Calculating the left side:
\[ \frac{33,940.50}{25,500} \approx 1.333 \]

6. **Take the Cube Root of Both Sides:**
\[ 1 + \frac{r}{100} = (1.333)^{\frac{1}{3}} \]
Calculating the cube root:
\[ 1 + \frac{r}{100} \approx 1.1 \]

7. **Isolate the Rate (r):**
\[ \frac{r}{100} = 1.1 - 1 = 0.1 \]
Multiplying both sides by 100:
\[ r = 0.1 \times 100 = 10 \]

8. **Conclusion:**
The rate of interest is \( r = 10\% \).

### Final Answer:
The rate of interest is **10%**.