Question

If the interest earned on a sum of money invested for 3 years at the annual interest rate of \(10\%\) compounded annually is Rs.14,895, then what is the sum of money invested?

• A. Rs.45,000
• B. Rs.42,500
• C. Rs.36,000
• D. Rs.48,000

Answer 1

The Correct Option is A

Compound Interest Calculation 

Step 1: Define the Compound Interest Formula

We use the compound interest formula to solve this problem:

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

• A is the amount (Principal + Interest),
• P is the principal (the sum of money invested),
• r is the annual interest rate,
• t is the time in years.

Step 2: Given Information

We are given the following:

• Interest earned: Rs. 14,895
• Annual interest rate (r): 10%
• Time (t): 3 years

Step 3: Calculate the Total Amount (A)

The total amount A is the principal P plus the interest earned, so:

\[ A = P + 14,895 \]

Step 4: Substitute into the Compound Interest Formula

Substitute into the compound interest formula:

\[ P + 14,895 = P \left(1 + \frac{10}{100}\right)^3 \] \[ P + 14,895 = P \times (1.1)^3 \] \[ P + 14,895 = P \times 1.331 \]

Step 5: Solve for P

\[ P \times 1.331 - P = 14,895 \] \[ P(1.331 - 1) = 14,895 \] \[ P \times 0.331 = 14,895 \] \[ P = \frac{14,895}{0.331} \approx 45,000 \]

Final Answer:

The sum of money invested is Rs. 45,000.

Conclusion:

The correct answer is (a) Rs. 45,000.