If in 2 years at simple interest the principal increases by `16%`, what will be the compound interest earned (in Rs.) on `Rs. 25,000` in 2 years at the same rate?

Options

A. `4000`
B. `2160`
C. `2000 `
D. `4160 `

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We know that in 2 years, the principal amount increases by 16% due to simple interest. We need to find out the compound interest earned on Rs. 25,000 in 2 years at the same rate of interest.

### Step 2: Find the Rate of Interest
Since the principal increases by 16% in 2 years, we can find the rate of interest per year.

- Total increase in 2 years = 16%
- Therefore, the rate of interest per year = 16% / 2 = 8%

### Step 3: Calculate the Compound Interest
Now, we will use the formula for compound interest to find the amount after 2 years. The formula for the amount (A) in compound interest is:

\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Where:
- \(P\) = Principal amount = Rs. 25,000
- \(r\) = Rate of interest = 8%
- \(t\) = Time in years = 2

Substituting the values into the formula:

\[ A = 25000 \left(1 + \frac{8}{100}\right)^2 \]

\[ A = 25000 \left(1 + 0.08\right)^2 \]

\[ A = 25000 \left(1.08\right)^2 \]

### Step 4: Calculate \( (1.08)^2 \)
Now we calculate \( (1.08)^2 \):

\[ (1.08)^2 = 1.1664 \]

### Step 5: Calculate the Amount
Now, substituting back into the amount formula:

\[ A = 25000 \times 1.1664 \]

\[ A = 29160 \]

### Step 6: Calculate the Compound Interest
Now, to find the compound interest (CI), we subtract the principal from the amount:

\[ CI = A - P \]

\[ CI = 29160 - 25000 \]

\[ CI = 4160 \]

### Final Answer
The compound interest earned on Rs. 25,000 in 2 years at the same rate is **Rs. 4,160**.

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