A sum of money on compound interest amount to Rs. 9680 in 2 years and to Rs. 10648 in 3 years. What is the rate of interest per annum?

Answer

To find the rate of interest per annum given that a sum of money amounts to Rs. 9680 in 2 years and Rs. 10648 in 3 years under compound interest, we can follow these steps:

### Step 1: Understand the relationship between amounts
We know that the amount after 2 years (A2) is Rs. 9680 and the amount after 3 years (A3) is Rs. 10648. The amount after 3 years can be expressed in terms of the amount after 2 years.

### Step 2: Set up the equation
Using the formula for compound interest, we can express the amount after 3 years as:
\[ A3 = A2 \times (1 + \frac{R}{100}) \]
Where:
- A3 = Rs. 10648
- A2 = Rs. 9680
- R = rate of interest per annum

### Step 3: Substitute the values into the equation
Substituting the values we have:
\[ 10648 = 9680 \times (1 + \frac{R}{100}) \]

### Step 4: Solve for (1 + R/100)
To isolate (1 + R/100), divide both sides by 9680:
\[ 1 + \frac{R}{100} = \frac{10648}{9680} \]

### Step 5: Calculate the right-hand side
Calculating the right-hand side:
\[ \frac{10648}{9680} = 1.1 \]
So we have:
\[ 1 + \frac{R}{100} = 1.1 \]

### Step 6: Isolate R
Now, subtract 1 from both sides:
\[ \frac{R}{100} = 1.1 - 1 \]
\[ \frac{R}{100} = 0.1 \]

### Step 7: Solve for R
Multiply both sides by 100 to find R:
\[ R = 0.1 \times 100 \]
\[ R = 10 \]

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

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