If compound interest on some amount at the rate of 15% interest for 3 years is 83.34 then find the principle amount?

Options

A. ₹ 145
B. ₹ 150
C. ₹ 155
D. ₹160

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
- \( n \) = Number of Years

Given:
- \( CI = 83.34 \)
- \( R = 15\% \)
- \( n = 3 \)

### Step 1: Rewrite the formula for CI
We can rearrange the formula to express it in terms of \( P \):

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

### Step 2: Substitute the known values
Substituting the known values into the formula, we get:

\[ 83.34 = P \left( \left(1 + \frac{15}{100}\right)^3 - 1 \right) \]

### Step 3: Calculate \( \left(1 + \frac{15}{100}\right)^3 \)
Calculating \( 1 + \frac{15}{100} \):

\[ 1 + \frac{15}{100} = 1 + 0.15 = 1.15 \]

Now, calculate \( (1.15)^3 \):

\[ (1.15)^3 = 1.15 \times 1.15 \times 1.15 = 1.520875 \]

### Step 4: Substitute back into the equation
Now substitute this value back into the equation:

\[ 83.34 = P \left( 1.520875 - 1 \right) \]

This simplifies to:

\[ 83.34 = P \times 0.520875 \]

### Step 5: Solve for \( P \)
Now, we can solve for \( P \):

\[ P = \frac{83.34}{0.520875} \]

Calculating this gives:

\[ P \approx 160 \]

### Final Answer
The principal amount \( P \) is approximately **160**.

---