If the amount received at the end of 2nd and 3rd year at Compound Interest on a cerLain Principal is Rs. 1,800, and Rs. 1.926 respectively, what is the rate of interest?

Options

A. 0.075
B. 0.07
C. 0.06
D. 0.065

Answer

To solve the problem, we need to find the rate of interest (r) given the amounts received at the end of the 2nd and 3rd years at compound interest.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- Let the principal amount be \( P \).
- The amount at the end of the 2nd year is \( A_2 = 1800 \).
- The amount at the end of the 3rd year is \( A_3 = 1926 \).

2. **Using the Formula for Compound Interest:**
- The formula for the amount at the end of \( n \) years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
- For the 2nd year:
\[ A_2 = P \left(1 + \frac{r}{100}\right)^2 = 1800 \]
- For the 3rd year:
\[ A_3 = P \left(1 + \frac{r}{100}\right)^3 = 1926 \]

3. **Setting Up the Equations:**
- From the above equations, we can express \( A_3 \) in terms of \( A_2 \):
\[ A_3 = A_2 \left(1 + \frac{r}{100}\right) \]
- Substituting the values:
\[ 1926 = 1800 \left(1 + \frac{r}{100}\right) \]

4. **Solving for \( r \):**
- Rearranging the equation:
\[ 1 + \frac{r}{100} = \frac{1926}{1800} \]
- Calculating \( \frac{1926}{1800} \):
\[ 1 + \frac{r}{100} = 1.07 \]
- Therefore:
\[ \frac{r}{100} = 1.07 - 1 = 0.07 \]
- Multiplying both sides by 100:
\[ r = 0.07 \times 100 = 7 \]

5. **Final Answer:**
- The rate of interest \( r \) is \( 7\% \).