The interest earned on amount after 2 years at `20%` pa compound yearly is ₹1716.find interest earned on same amount after 3 years at `15%` pa at simple rate of interest

Options

A. `₹1620`
B. `₹1755`
C. `₹1665`
D. `₹1710`

Answer

To solve the problem step by step, we will first find the principal amount using the compound interest information provided, and then use that principal to calculate the simple interest for the next part of the question.

### Step 1: Find the Principal Amount (P)

Given:
- Compound Interest (CI) after 2 years = ₹1716
- Rate of interest (R) = 20% per annum
- Time (T) = 2 years

Using the formula for compound interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where \( A \) is the total amount after time \( T \), and \( P \) is the principal amount.

We know that:
\[ A = P + CI \]
So,
\[ A = P + 1716 \]

Substituting into the compound interest formula:
\[ P + 1716 = P \left(1 + \frac{20}{100}\right)^2 \]

Calculating \( \left(1 + \frac{20}{100}\right)^2 \):
\[ \left(1 + 0.2\right)^2 = (1.2)^2 = 1.44 \]

Now substituting back:
\[ P + 1716 = P \times 1.44 \]

Rearranging gives:
\[ 1716 = P \times 1.44 - P \]
\[ 1716 = P(1.44 - 1) \]
\[ 1716 = P(0.44) \]

Now, solving for \( P \):
\[ P = \frac{1716}{0.44} \]
\[ P = 3900 \]

### Step 2: Calculate Simple Interest (SI)

Now that we have the principal amount, we can calculate the simple interest for 3 years at 15% per annum.

Given:
- Principal (P) = ₹3900
- Rate of interest (R) = 15% per annum
- Time (T) = 3 years

Using the formula for simple interest:
\[ SI = \frac{P \times R \times T}{100} \]

Substituting the values:
\[ SI = \frac{3900 \times 15 \times 3}{100} \]

Calculating:
\[ SI = \frac{3900 \times 45}{100} \]
\[ SI = \frac{175500}{100} \]
\[ SI = 1755 \]

### Final Answer:
The interest earned on the same amount after 3 years at 15% per annum at simple rate of interest is **₹1755**.

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