An amount of money grows upto Rs. 4840 in 2 years and upto Rs. 5324 in 3 years on compound interest.Find the rate per cent.

Answer

To solve the problem, we need to find the rate of interest per annum when an amount grows from Rs. 4840 in 2 years to Rs. 5324 in 3 years under compound interest.

### Step 1: Identify the amounts
- Amount after 2 years (A2) = Rs. 4840
- Amount after 3 years (A3) = Rs. 5324

### Step 2: Calculate the interest earned in the 3rd year
The interest earned in the 3rd year can be calculated as:
\[ \text{Interest in 3rd year} = A3 - A2 \]
\[ \text{Interest in 3rd year} = 5324 - 4840 = 484 \]

### Step 3: Use the interest to find the principal
Let the principal amount be \( P \) and the rate of interest be \( r \% \).

The amount after 2 years can be expressed using the compound interest formula:
\[ A2 = P \left(1 + \frac{r}{100}\right)^2 \]
Substituting the known value:
\[ 4840 = P \left(1 + \frac{r}{100}\right)^2 \] (1)

The amount after 3 years can be expressed as:
\[ A3 = P \left(1 + \frac{r}{100}\right)^3 \]
Substituting the known value:
\[ 5324 = P \left(1 + \frac{r}{100}\right)^3 \] (2)

### Step 4: Relate the two equations
From equations (1) and (2), we can express \( A3 \) in terms of \( A2 \):
\[ A3 = A2 \times \left(1 + \frac{r}{100}\right) \]
Substituting the values:
\[ 5324 = 4840 \times \left(1 + \frac{r}{100}\right) \]

### Step 5: Solve for \( r \)
Now, we can solve for \( r \):
\[ 1 + \frac{r}{100} = \frac{5324}{4840} \]
Calculating the right side:
\[ \frac{5324}{4840} = 1.1 \]
Thus,
\[ 1 + \frac{r}{100} = 1.1 \]
Subtracting 1 from both sides:
\[ \frac{r}{100} = 0.1 \]
Multiplying by 100:
\[ r = 10 \]

### Final Answer
The rate of interest per annum is **10%**.

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