Interest earned on an amount after 2 years at 20% p.a compounded yearly is ₹3432. Find the interest earned on same amount after 3 years at 15% p.a. at simple interest.

Options

A. ₹1,620
B. ₹3,510
C. ₹1,665
D. ₹1,710

Explanation

To solve the problem step-by-step, we need to find the principal amount first using the information given about the compound interest, and then calculate the simple interest for the same amount.

### Step 1: Find the Principal Amount
We know that the interest earned after 2 years at 20% per annum compounded yearly is ₹3432. We can use the formula for compound interest to find the principal amount (P).

The formula for compound interest is:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the total amount after n years,
- \( P \) is the principal amount,
- \( r \) is the rate of interest (in decimal),
- \( n \) is the number of years.

The interest earned can be expressed as:
\[ \text{Interest} = A - P \]
So, we can rewrite the equation:
\[ 3432 = P(1 + 0.20)^2 - P \]
This simplifies to:
\[ 3432 = P(1.44 - 1) \]
\[ 3432 = P(0.44) \]

Now, we can solve for \( P \):
\[ P = \frac{3432}{0.44} \]
\[ P = 7800 \]

### Step 2: Calculate Simple Interest
Now that we have the principal amount, we need to find the simple interest earned on this amount after 3 years at a rate of 15% per annum.

The formula for simple interest (SI) is:
\[ SI = \frac{P \times r \times t}{100} \]
Where:
- \( P = 7800 \) (the principal amount),
- \( r = 15\% \) (the rate of interest),
- \( t = 3 \) (the time period in years).

Substituting the values into the formula:
\[ SI = \frac{7800 \times 15 \times 3}{100} \]
\[ SI = \frac{351000}{100} \]
\[ SI = 3510 \]

### Final Answer
The interest earned on the same amount after 3 years at 15% per annum at simple interest is ₹3510.

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