Renuka borrowed Rs.15,000 from Vipul at 5% per annum at simple interest for 3 years. If she had borrowed this sum at same rate and time at compound interest, then what extra amount would she has to pay?

Options

A. Rs.114.38
B. Rs.1483
C. Rs.483.20
D. Rs.43.20

Answer

To solve the problem, we need to calculate the total amount Renuka would pay using both simple interest and compound interest, and then find the difference between the two amounts.

### Step 1: Calculate Simple Interest (SI)

The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 15,000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time (3 years)

Substituting the values:
\[ SI = \frac{15000 \times 5 \times 3}{100} \]
\[ SI = \frac{225000}{100} \]
\[ SI = 2250 \]

### Step 2: Calculate Total Amount with Simple Interest

The total amount (A) paid after 3 years with Simple Interest is:
\[ A = P + SI \]
Substituting the values:
\[ A = 15000 + 2250 \]
\[ A = 17250 \]

### Step 3: Calculate Compound Interest (CI)

The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Substituting the values:
\[ A = 15000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 15000 \left(1 + 0.05\right)^3 \]
\[ A = 15000 \left(1.05\right)^3 \]

Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]
Now substituting back:
\[ A = 15000 \times 1.157625 \]
\[ A \approx 17364.38 \]

### Step 4: Calculate the Extra Amount Paid

The extra amount paid when borrowing at Compound Interest compared to Simple Interest is:
\[ \text{Extra Amount} = A_{CI} - A_{SI} \]
Substituting the values:
\[ \text{Extra Amount} = 17364.38 - 17250 \]
\[ \text{Extra Amount} \approx 114.38 \]

### Final Answer

Renuka would have to pay approximately Rs. 114.38 extra if she borrowed the sum at compound interest instead of simple interest.

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