Question

A sum of money is invested at compound interest for 3 years. However, the rate of interest is\(10\%\)for first year,\(15\%\)for second year and\(20\%\)for third year. If the total interest earned is Rs.15,540, then what was the sum of money invested?

• A. Rs.25,000
• B. Rs.40,000
• C. Rs.30,000
• D. Rs.36,000

Answer 1

The Correct Option is C

Calculation of Principal Amount 

Step 1: Interest Calculation for Each Year

- Let the principal amount be P.

- The interest for the first year is 10% of P:

\[ I_1 = \frac{10}{100} \times P = 0.1P \]

- After the first year, the new principal becomes:

\[ P + I_1 = P + 0.1P = 1.1P \]

- The interest for the second year is 15% of the new principal:

\[ I_2 = \frac{15}{100} \times 1.1P = 0.165P \]

- After the second year, the new principal becomes:

\[ 1.1P + I_2 = 1.1P + 0.165P = 1.265P \]

- The interest for the third year is 20% of the new principal:

\[ I_3 = \frac{20}{100} \times 1.265P = 0.253P \]

Step 2: Calculate Total Interest

The total interest over 3 years is the sum of all interests:

\[ I_{\text{total}} = 0.1P + 0.165P + 0.253P = 0.518P \]

Step 3: Finding the Principal

We are given that the total interest is Rs. 15,540:

\[ 0.518P = 15,540 \]

Solving for P:

\[ P = \frac{15,540}{0.518} = 30,000 \]

Conclusion:

The sum of money invested is Rs. 30,000.