Aarti has to pay Rs 440 to Babita after
1 yr. Babita asks Aarti to pay RS 220 in cash and defer the payment of RS 220 for
2 yr. Aarti agrees to it. If the rate of interest be 10% per annum, find Aarti's gain or loss.

Options

A. Aarti gains X 3.33
B. Aarti gains X 8
C. Aarti losses X 9
D. Aarti losses X 3.33

Answer

To solve the problem step by step, we will calculate Aarti's gain or loss based on the payments made and the present worth of the amounts involved.

### Step 1: Understand the Payments
Aarti has to pay Rs. 440 to Babita after 1 year. Babita allows Aarti to pay Rs. 220 in cash now and defer the payment of Rs. 220 for 2 years.

### Step 2: Calculate the Present Worth of Rs. 440
We need to find the present worth (PW) of Rs. 440 due after 1 year at an interest rate of 10% per annum.

The formula for present worth is:
\[ PW = \frac{FV}{(1 + r)^t} \]
Where:
- \(FV\) = Future Value (Rs. 440)
- \(r\) = Rate of interest (10% or 0.10)
- \(t\) = Time in years (1 year)

Substituting the values:
\[ PW = \frac{440}{(1 + 0.10)^1} = \frac{440}{1.10} = 400 \]

### Step 3: Calculate the Present Worth of Rs. 220 Deferred for 2 Years
Next, we calculate the present worth of the Rs. 220 that Aarti will pay after 2 years.

Using the same formula:
\[ PW = \frac{FV}{(1 + r)^t} \]
Where:
- \(FV\) = Future Value (Rs. 220)
- \(r\) = Rate of interest (10% or 0.10)
- \(t\) = Time in years (2 years)

Substituting the values:
\[ PW = \frac{220}{(1 + 0.10)^2} = \frac{220}{1.21} \approx 181.82 \]

### Step 4: Calculate Total Payment Made by Aarti
Aarti pays Rs. 220 in cash now and the present worth of the deferred payment is approximately Rs. 181.82.

Total payment made by Aarti:
\[ \text{Total Payment} = 220 + 181.82 \approx 401.82 \]

### Step 5: Calculate Gain or Loss
Now, we compare the total payment made by Aarti with the present worth of Rs. 440.

Gain or Loss = Present Worth of Rs. 440 - Total Payment
\[ \text{Gain or Loss} = 400 - 401.82 \approx -1.82 \]

Since the result is negative, Aarti incurs a loss of approximately Rs. 1.82.

### Final Answer
Aarti's loss is approximately Rs. 1.82.

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