At what rate precent will Rs 2000 amount to Rs 2315.25 in 3 years at compound interest ?

Options

A. `5%`
B. `7%`
C. `12%`
D. `15%`

Answer

To find the rate percent at which Rs 2000 will amount to Rs 2315.25 in 3 years at compound interest, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Where:
- \( A \) = Amount after time \( T \) (Rs 2315.25)
- \( P \) = Principal amount (Rs 2000)
- \( R \) = Rate of interest (unknown)
- \( T \) = Time in years (3 years)

### Step 1: Substitute the known values into the formula

Substituting the values we have:

\[ 2315.25 = 2000 \left(1 + \frac{R}{100}\right)^3 \]

### Step 2: Divide both sides by 2000

To isolate the term with \( R \):

\[ \frac{2315.25}{2000} = \left(1 + \frac{R}{100}\right)^3 \]

Calculating the left side:

\[ 1.157625 = \left(1 + \frac{R}{100}\right)^3 \]

### Step 3: Take the cube root of both sides

To eliminate the exponent, we take the cube root:

\[ \sqrt[3]{1.157625} = 1 + \frac{R}{100} \]

Calculating the cube root:

\[ 1.05 = 1 + \frac{R}{100} \]

### Step 4: Solve for \( R \)

Now, we can isolate \( R \):

\[ \frac{R}{100} = 1.05 - 1 \]

\[ \frac{R}{100} = 0.05 \]

Multiplying both sides by 100:

\[ R = 5 \]

### Conclusion

The rate percent \( R \) is **5%**.

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