Question

At what rate of compound interest per annum, a sum of Rs 1800 becomes Rs 2178 in two years?

• A. 13%
• B. 12%
• C. 11%
• D. 10%

Hint:

Use \(A = P(1 + r/100)^2\). The ratio \(2178/1800\) simplifies to \(121/100\), a perfect square.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
A principal of Rs. 1800 grows to Rs. 2178 in two years under compound interest. We must find the yearly rate.

Step 2: Key Formula or Approach:
For compound interest with yearly compounding, the amount is
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Here \(P = 1800\), \(A = 2178\) and \(n = 2\).

Step 3: Set up the equation:
\[ 2178 = 1800 \left(1 + \frac{r}{100}\right)^2 \]
\[ \left(1 + \frac{r}{100}\right)^2 = \frac{2178}{1800} = \frac{121}{100} \]

Step 4: Solve for r:
Take the square root of both sides.
\[ 1 + \frac{r}{100} = \frac{11}{10} \]
\[ \frac{r}{100} = \frac{1}{10} \Rightarrow r = 10 \]

Step 5: Check the options:
With 10 percent, year 1 gives \(1800 \times 1.1 = 1980\), and year 2 gives \(1980 \times 1.1 = 2178\). This matches. With 11 percent the amount would be \(1800 \times 1.2321 = 2217.78\), with 12 percent it would be 2257.92 and with 13 percent it would be 2298.42. These do not match, so options (1), (2) and (3) are wrong.

Final Answer:
The rate of compound interest is 10 percent per annum. This is option (4). \[ \boxed{10 \%} \]