A sum becomes Rs. 2916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be

Answer

To solve the problem step by step, we will first find the principal amount using the compound interest formula, and then we will calculate the simple interest based on that principal amount.

### Step 1: Identify the given values
- Amount (A) = Rs. 2916
- Time (t) = 2 years
- Rate (r) = 8% per annum

### Step 2: Use the compound interest formula to find the principal (P)
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Rearranging this to find P gives us:
\[ P = \frac{A}{\left(1 + \frac{r}{100}\right)^t} \]

Substituting the known values:
\[ P = \frac{2916}{\left(1 + \frac{8}{100}\right)^2} \]
\[ P = \frac{2916}{\left(1 + 0.08\right)^2} \]
\[ P = \frac{2916}{(1.08)^2} \]
\[ P = \frac{2916}{1.1664} \]
\[ P = 2500 \]

### Step 3: Calculate the simple interest (SI) for 3 years at 9%
The formula for simple interest is:
\[ SI = \frac{P \times r \times t}{100} \]

Substituting the values:
- Principal (P) = Rs. 2500
- Rate (r) = 9%
- Time (t) = 3 years

Calculating the simple interest:
\[ SI = \frac{2500 \times 9 \times 3}{100} \]
\[ SI = \frac{67500}{100} \]
\[ SI = 675 \]

### Final Answer
The simple interest at 9% per annum for 3 years on the same amount is Rs. 675.

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