There is 100% increase in an amount in 15 year at simple interest. Find the compound interest of ₹2250 after 2 year at the same rate of interest.

Options

A. 310
B. 300
C. 345
D. 375

Answer

To solve the problem, we need to follow these steps:

### Step 1: Determine the rate of interest
Given that there is a 100% increase in an amount in 15 years at simple interest, we can deduce that the final amount (A) is double the principal (P).

Let the principal amount (P) be ₹100 (for simplicity).
- After 15 years, the amount A = P + SI
- Since there is a 100% increase, A = 2P = ₹200.

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

Substituting the values we have:
\[ 200 - 100 = \frac{100 \times R \times 15}{100} \]
\[ 100 = \frac{100 \times R \times 15}{100} \]
\[ 100 = R \times 15 \]
\[ R = \frac{100}{15} = \frac{20}{3} \approx 6.67\% \]

### Step 2: Calculate the compound interest for ₹2250 after 2 years
Now that we have the rate of interest (R = 20/3%), we can calculate the compound interest (CI) for ₹2250 after 2 years using the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- A = Amount after time T
- P = Principal amount (₹2250)
- R = Rate of interest (20/3%)
- T = Time (2 years)

Substituting the values:
\[ A = 2250 \left(1 + \frac{20/3}{100}\right)^2 \]
\[ A = 2250 \left(1 + \frac{20}{300}\right)^2 \]
\[ A = 2250 \left(1 + \frac{1}{15}\right)^2 \]
\[ A = 2250 \left(\frac{16}{15}\right)^2 \]
\[ A = 2250 \times \frac{256}{225} \]
\[ A = 2560 \]

### Step 3: Calculate the compound interest
Now, we can find the compound interest (CI) using the formula:
\[ CI = A - P \]
\[ CI = 2560 - 2250 \]
\[ CI = 310 \]

### Final Answer
The compound interest of ₹2250 after 2 years at the same rate of interest is **₹310**.

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