The compound interest accrued on an amount at the end of two years @16% p.a is Rs. 3041.28. What is the amount ?

Options

A. Rs. 10,500 /-
B. Rs. 9,000 /-
C. Rs. 7,250 /-
D. Rs. 8,800 /-

Answer

To find the principal amount (P) from the compound interest accrued over two years, we can use the formula for compound interest for two years:

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

Where:
- \( CI \) is the compound interest
- \( P \) is the principal amount
- \( r \) is the rate of interest per annum
- \( n \) is the number of years

Given:
- \( CI = 3041.28 \)
- \( r = 16\% \)
- \( n = 2 \)

### Step 1: Calculate the total amount after 2 years

We can rewrite the formula for compound interest as:

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

Substituting the known values:

\[ 3041.28 = P \left( \left(1 + \frac{16}{100}\right)^2 - 1 \right) \]

### Step 2: Calculate \( \left(1 + \frac{16}{100}\right)^2 \)

First, calculate \( 1 + \frac{16}{100} = 1.16 \).

Now, square it:

\[ 1.16^2 = 1.3456 \]

### Step 3: Substitute back into the equation

Now substitute this back into the equation:

\[ 3041.28 = P \left( 1.3456 - 1 \right) \]

This simplifies to:

\[ 3041.28 = P \times 0.3456 \]

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

Now, isolate \( P \):

\[ P = \frac{3041.28}{0.3456} \]

Calculating this gives:

\[ P = 8800 \]

### Final Answer

The principal amount is Rs. 8800.

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