Find C.I on Rs 10000 at the rate of interest 6%, for , `1(1)/(2)` years, compoun annually.

Answer

To find the Compound Interest (C.I) on Rs 10,000 at the rate of 6% for 1.5 years compounded annually, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Principal (P) = Rs 10,000
- Rate of interest (R) = 6% per annum
- Time (T) = 1.5 years

**Hint:** Always start by noting down the values provided in the question.

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**Step 2: Calculate the amount after 1.5 years using the compound interest formula.**
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal
- \( R \) = Rate of interest
- \( T \) = Time in years

Substituting the values:
\[ A = 10000 \left(1 + \frac{6}{100}\right)^{1.5} \]

**Hint:** Remember to convert the percentage into a decimal by dividing by 100.

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**Step 3: Simplify the expression inside the parentheses.**
\[ A = 10000 \left(1 + 0.06\right)^{1.5} \]
\[ A = 10000 \left(1.06\right)^{1.5} \]

**Hint:** Calculate \( 1 + \frac{R}{100} \) first before raising it to the power of \( T \).

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**Step 4: Calculate \( (1.06)^{1.5} \).**
Using a calculator:
\[ (1.06)^{1.5} \approx 1.090454 \]

Now substituting back into the equation:
\[ A \approx 10000 \times 1.090454 \]
\[ A \approx 10904.54 \]

**Hint:** Use a calculator for exponentiation to ensure accuracy.

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**Step 5: Calculate the Compound Interest (C.I).**
To find the compound interest, subtract the principal from the amount:
\[ C.I = A - P \]
\[ C.I = 10904.54 - 10000 \]
\[ C.I \approx 904.54 \]

**Hint:** The compound interest is the total amount minus the initial principal.

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### Final Answer:
The Compound Interest on Rs 10,000 at the rate of 6% for 1.5 years compounded annually is approximately Rs 904.54.

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