Jalela and Dalela have to clear their respective loans by paying 3 equal annual instalments of Rs. 30000 each . Jalela pays @ 10% per annum of simple interest while Dalela pays 10% per annum compound interest. What is the difference in their payments ?

Options

A. A). Rs. 300
B. B). Rs. 425
C. C). Rs. 245
D. D). Rs. 333.33

Answer

To solve the problem, we need to calculate the total payments made by Jalela and Dalela over the three years and then find the difference between their total payments.

### Step 1: Calculate Jalela's Total Payment

Jalela pays 3 equal annual installments of Rs. 30,000 each at a simple interest rate of 10% per annum.

1. **First Installment**:
- Paid at the end of Year 1: Rs. 30,000 (No interest as it is paid immediately)

2. **Second Installment**:
- Paid at the end of Year 2: Rs. 30,000
- Interest for 1 year on this installment = Principal × Rate × Time = 30,000 × 10% × 1 = Rs. 3,000

3. **Third Installment**:
- Paid at the end of Year 3: Rs. 30,000
- Interest for 2 years on this installment = Principal × Rate × Time = 30,000 × 10% × 2 = Rs. 6,000

**Total Payment by Jalela**:
\[ \text{Total Payment} = \text{First Installment} + \text{Second Installment} + \text{Third Installment} + \text{Interest on Second Installment} + \text{Interest on Third Installment} \]
\[ \text{Total Payment} = 30,000 + 30,000 + 30,000 + 3,000 + 6,000 = 99,000 \]

### Step 2: Calculate Dalela's Total Payment

Dalela pays 3 equal annual installments of Rs. 30,000 each at a compound interest rate of 10% per annum.

1. **First Installment**:
- Paid at the end of Year 1: Rs. 30,000 (No interest as it is paid immediately)

2. **Second Installment**:
- Paid at the end of Year 2: Rs. 30,000
- Interest for 1 year on this installment = Rs. 30,000 (Principal) × (1 + 10%)^1 - Rs. 30,000 = Rs. 3,000

3. **Third Installment**:
- Paid at the end of Year 3: Rs. 30,000
- Interest for 2 years on this installment = Rs. 30,000 (Principal) × (1 + 10%)^2 - Rs. 30,000
- Calculation:
\[ 30,000 \times (1.1)^2 - 30,000 = 30,000 \times 1.21 - 30,000 = 36,300 - 30,000 = 6,300 \]

**Total Payment by Dalela**:
\[ \text{Total Payment} = \text{First Installment} + \text{Second Installment} + \text{Third Installment} + \text{Interest on Second Installment} + \text{Interest on Third Installment} \]
\[ \text{Total Payment} = 30,000 + 30,000 + 30,000 + 3,000 + 6,300 = 99,300 \]

### Step 3: Calculate the Difference in Payments

Now we find the difference between Jalela's and Dalela's total payments.

\[ \text{Difference} = \text{Total Payment by Dalela} - \text{Total Payment by Jalela} \]
\[ \text{Difference} = 99,300 - 99,000 = 300 \]

### Final Answer

The difference in their payments is Rs. 300.

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