A sum amounts to Rs 1210 in 2 years when invested at compound interest. If principal is Rs 1000, then what is the rate of interest (in %)?

Options

A. a. 10
B. b. 20
C. c. 15
D. d. 12

Answer

To find the rate of interest when a sum amounts to Rs 1210 in 2 years with a principal of Rs 1000 at compound interest, we can follow these steps:

### Step 1: Understand the Compound Interest Formula
The formula for the amount \( A \) in compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
where:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest (in %)
- \( n \) = Time (in years)

### Step 2: Substitute the Known Values
In this case, we know:
- \( A = 1210 \)
- \( P = 1000 \)
- \( n = 2 \)

Substituting these values into the formula gives:
\[ 1210 = 1000 \left(1 + \frac{R}{100}\right)^2 \]

### Step 3: Simplify the Equation
To isolate the term with \( R \), divide both sides by 1000:
\[ \frac{1210}{1000} = \left(1 + \frac{R}{100}\right)^2 \]
This simplifies to:
\[ 1.21 = \left(1 + \frac{R}{100}\right)^2 \]

### Step 4: Take the Square Root
Next, we take the square root of both sides:
\[ \sqrt{1.21} = 1 + \frac{R}{100} \]
Calculating the square root gives:
\[ 1.1 = 1 + \frac{R}{100} \]

### Step 5: Solve for \( R \)
Now, subtract 1 from both sides:
\[ 1.1 - 1 = \frac{R}{100} \]
This simplifies to:
\[ 0.1 = \frac{R}{100} \]
Multiplying both sides by 100 gives:
\[ R = 10 \]

### Conclusion
The rate of interest \( R \) is \( 10\% \).