A sum of money amounts to `Rs. 6655` at the rate of `10% ` compounded annually for 3 years. The sum of money is

Options

A. `Rs. 5000 `
B. `Rs. 5500 `
C. `Rs. 6000`
D. `Rs. 6100`

Answer

To find the principal amount (the sum of money) that amounts to Rs. 6655 at a rate of 10% compounded annually for 3 years, we can use the formula for compound interest. The formula for the amount \( A \) after \( n \) years is given by:

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

Where:
- \( A \) = Amount after \( n \) years
- \( P \) = Principal amount (the initial sum of money)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

### Step 1: Identify the values
From the question, we have:
- \( A = 6655 \)
- \( r = 10\% \)
- \( n = 3 \)

### Step 2: Substitute the values into the formula
We need to rearrange the formula to solve for \( P \):

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

Substituting the known values:

\[ P = \frac{6655}{\left(1 + \frac{10}{100}\right)^3} \]

### Step 3: Simplify the expression
Calculating \( 1 + \frac{10}{100} \):

\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]

Now we need to calculate \( (1.1)^3 \):

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

### Step 4: Substitute back to find \( P \)
Now substitute \( (1.1)^3 \) back into the equation for \( P \):

\[ P = \frac{6655}{1.331} \]

### Step 5: Calculate \( P \)
Now, performing the division:

\[ P \approx 5000 \]

### Conclusion
Thus, the principal amount (the sum of money) is approximately Rs. 5000.

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