Question

A sum of money invested at compound interest amounts to Rs.15,000 in one year and Rs.16,500 in two years. Then the rate of interest is

• A. 8\%
• B. 10\%
• C. 12\%
• D. 15\%

Hint:

For successive compound amounts, divide consecutive amounts to directly find the rate.

Answer 1

The Correct Option is B

To determine the rate of compound interest, we are given that the amount becomes Rs. 15,000 in one year and Rs. 16,500 in two years. Let's solve this step-by-step:

1. The amount after one year is Rs. 15,000, and after two years, it is Rs. 16,500. This implies: \(A_1 = 15,000\) and \(A_2 = 16,500\).
2. The formula for compound interest is: \(A = P (1 + \frac{R}{100})^n\) where \(P\) is the principal amount, \(R\) is the rate of interest, and \(n\) is the time period in years.
3. The relationship between the amounts for consecutive years when compounded annually is given by: \(\frac{A_2}{A_1} = 1 + \frac{R}{100}\).
4. Substituting the values we know: \(\frac{16,500}{15,000} = 1 + \frac{R}{100}\).
5. Simplifying the fraction gives: \(1.1 = 1 + \frac{R}{100}\).
6. Subtract 1 from both sides to isolate the fraction: \(\frac{R}{100} = 0.1\).
7. Finally, multiply both sides by 100 to solve for \(R\): \(R = 10\%\).

Thus, the correct rate of interest is 10%.