A person borrowed Rs 32,000 at a yearly 9% simple interest and deposited the same amount in a bank at a yearly 1 compound interest of 10%. What is the gain in rupees at the end of 3 years?

Options

A. Rs 926
B. Rs 1,904
C. Rs 2,904
D. Rs 1,952

Answer

To solve the problem step by step, we will calculate the simple interest (SI) on the borrowed amount and the compound interest (CI) on the deposited amount, then find the gain.

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs 32,000)
- \( R \) = Rate of interest (9%)
- \( T \) = Time (3 years)

Substituting the values:
\[ \text{SI} = \frac{32000 \times 9 \times 3}{100} \]
\[ \text{SI} = \frac{864000}{100} \]
\[ \text{SI} = 8640 \]

### Step 2: Calculate Compound Interest (CI)
The formula for the amount \( A \) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( P \) = Principal amount (Rs 32,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (3 years)

Substituting the values:
\[ A = 32000 \left(1 + \frac{10}{100}\right)^3 \]
\[ A = 32000 \left(1 + 0.1\right)^3 \]
\[ A = 32000 \left(\frac{11}{10}\right)^3 \]
\[ A = 32000 \times \frac{1331}{1000} \]
\[ A = 32000 \times 1.331 \]
\[ A = 42656 \]

### Step 3: Calculate Compound Interest (CI)
Now, we can find the compound interest:
\[ \text{CI} = A - P \]
\[ \text{CI} = 42656 - 32000 \]
\[ \text{CI} = 10656 \]

### Step 4: Calculate Gain
The gain is the difference between the compound interest earned and the simple interest paid:
\[ \text{Gain} = \text{CI} - \text{SI} \]
\[ \text{Gain} = 10656 - 8640 \]
\[ \text{Gain} = 2016 \]

### Final Answer
The gain at the end of 3 years is Rs 2016.

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