If compound interest on some amount at the rate of 10% interest for 3 years is 4965 then find the principle amount?

Options

A. ₹ 17000
B. ₹ 15000
C. ₹ 14500
D. ₹ 16000

Answer

To find the principal amount when the compound interest (CI) is given, we can use the formula for compound interest:

\[ CI = P \left(1 + \frac{r}{100}\right)^n - P \]

Where:
- \( CI \) = Compound Interest
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

Given:
- \( CI = 4965 \)
- \( r = 10\% \)
- \( n = 3 \)

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

We can rearrange the formula to find \( P \):

\[ CI = P \left( \left(1 + \frac{r}{100}\right)^n - 1 \right) \]

Substituting the known values:

\[ 4965 = P \left( \left(1 + \frac{10}{100}\right)^3 - 1 \right) \]

### Step 2: Calculate \( \left(1 + \frac{10}{100}\right)^3 \)

First, calculate \( 1 + \frac{10}{100} = 1.1 \).

Now, raise it to the power of 3:

\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 3: Substitute back into the equation

Now we substitute back into the equation:

\[ 4965 = P \left( 1.331 - 1 \right) \]

This simplifies to:

\[ 4965 = P \times 0.331 \]

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

Now, we can solve for \( P \):

\[ P = \frac{4965}{0.331} \]

Calculating this gives:

\[ P \approx 15000 \]

### Final Answer

The principal amount \( P \) is approximately **15000**.

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