Roohi deposited Rs 7,000 in a finance company for 3 years at an interest of 15% per annum compounded annually. What is the compound interest and the amount that Roohi gets after 3 years ?

Answer

To solve the problem of Roohi's investment, we need to calculate the compound interest and the total amount she will receive after 3 years. Here’s how to do it step by step:

### Step 1: Identify the given values
- Principal (P) = Rs 7,000
- Rate of interest (R) = 15% per annum
- Time (T) = 3 years

### Step 2: Use the formula for compound amount
The formula to calculate the amount (A) after time T with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ A = 7000 \left(1 + \frac{15}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
Calculate \( 1 + \frac{15}{100} \):
\[ 1 + \frac{15}{100} = 1 + 0.15 = 1.15 \]

### Step 5: Raise the result to the power of 3
Now calculate \( (1.15)^3 \):
\[ (1.15)^3 = 1.15 \times 1.15 \times 1.15 \]

Calculating step by step:
1. \( 1.15 \times 1.15 = 1.3225 \)
2. \( 1.3225 \times 1.15 \approx 1.520875 \)

### Step 6: Calculate the total amount (A)
Now substitute back to find A:
\[ A = 7000 \times 1.520875 \]
\[ A \approx 10646.125 \]

### Step 7: Calculate the compound interest (CI)
The compound interest can be calculated using the formula:
\[ CI = A - P \]
Substituting the values:
\[ CI = 10646.125 - 7000 \]
\[ CI = 3646.125 \]

### Final Results
- The compound interest (CI) is approximately Rs 3646.13.
- The total amount (A) Roohi will receive after 3 years is approximately Rs 10646.13.

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