At what rate per cent per annum will ₹4500 amount to ₹5715 in 3 years?

Answer

To solve the problem of finding the rate of interest at which ₹4500 will amount to ₹5715 in 3 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = ₹4500
- Amount (A) = ₹5715
- Time (T) = 3 years

2. **Calculate Simple Interest (SI):**
- The formula for the amount is:
\[ A = P + SI \]
- Rearranging this, we can find the Simple Interest:
\[ SI = A - P \]
- Substituting the values:
\[ SI = 5715 - 4500 = 1215 \]

3. **Use the Simple Interest Formula:**
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- We know SI, P, and T, but we need to find R (rate of interest). Rearranging the formula gives:
\[ R = \frac{SI \times 100}{P \times T} \]

4. **Substitute the Known Values:**
- Now substitute the values of SI, P, and T into the formula:
\[ R = \frac{1215 \times 100}{4500 \times 3} \]

5. **Calculate the Denominator:**
- First, calculate \(4500 \times 3\):
\[ 4500 \times 3 = 13500 \]

6. **Calculate R:**
- Now substitute back into the equation:
\[ R = \frac{1215 \times 100}{13500} \]
- Simplifying this:
\[ R = \frac{121500}{13500} = 9 \]

7. **Final Result:**
- Therefore, the rate of interest is:
\[ R = 9\% \]