At what rate percent per annum C.I will Rs 2,000 amount to Rs 2,315.25 in 3 years ?

Answer

To find the rate percent per annum at which Rs 2,000 will amount to Rs 2,315.25 in 3 years using the compound interest formula, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs 2,000
- Amount (A) = Rs 2,315.25
- Time (T) = 3 years

2. **Use the Compound Interest Formula:**
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
where:
- A = Amount
- P = Principal
- r = Rate of interest per annum
- t = Time in years

3. **Substitute the Known Values into the Formula:**
\[ 2315.25 = 2000 \left(1 + \frac{r}{100}\right)^3 \]

4. **Divide Both Sides by 2000:**
\[ \frac{2315.25}{2000} = \left(1 + \frac{r}{100}\right)^3 \]
\[ 1.157625 = \left(1 + \frac{r}{100}\right)^3 \]

5. **Take the Cube Root of Both Sides:**
\[ \sqrt[3]{1.157625} = 1 + \frac{r}{100} \]
Calculating the cube root:
\[ 1.05 = 1 + \frac{r}{100} \]

6. **Isolate the Rate (r):**
\[ 1.05 - 1 = \frac{r}{100} \]
\[ 0.05 = \frac{r}{100} \]

7. **Multiply Both Sides by 100:**
\[ r = 0.05 \times 100 \]
\[ r = 5 \]

8. **Conclusion:**
The rate percent per annum is **5%**.