Bank A provides loan at 5% per annum at simple interest and Bank B provides loan at the same rate for the same period, compounded annually. Then, which bank is preferable for a person to take a loan ?

Answer

To determine which bank is preferable for a person to take a loan, we need to compare the total amount payable at the end of the loan period for both Bank A (which offers simple interest) and Bank B (which offers compound interest).

Let's assume the principal amount (P) is ₹1000 and the time period (T) is 2 years. The rate of interest (R) is 5% per annum for both banks.

### Step 1: Calculate the total amount payable to Bank A (Simple Interest)

1. **Formula for Simple Interest (SI)**:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- P = Principal amount
- R = Rate of interest
- T = Time in years

2. **Substituting the values**:
\[ SI = \frac{1000 \times 5 \times 2}{100} = \frac{10000}{100} = 100 \]

3. **Total Amount Payable to Bank A**:
\[ \text{Total Amount} = P + SI = 1000 + 100 = 1100 \]

### Step 2: Calculate the total amount payable to Bank B (Compound Interest)

1. **Formula for Compound Interest (CI)**:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- A = Total amount after time T
- P = Principal amount
- R = Rate of interest
- T = Time in years

2. **Substituting the values**:
\[ A = 1000 \left(1 + \frac{5}{100}\right)^2 = 1000 \left(1 + 0.05\right)^2 = 1000 \times (1.05)^2 \]

3. **Calculating (1.05)^2**:
\[ (1.05)^2 = 1.1025 \]

4. **Total Amount Payable to Bank B**:
\[ A = 1000 \times 1.1025 = 1102.5 \]

### Step 3: Compare the total amounts

- Total amount payable to Bank A = ₹1100
- Total amount payable to Bank B = ₹1102.5

### Conclusion

Since ₹1100 (Bank A) is less than ₹1102.5 (Bank B), it is preferable for a person to take a loan from **Bank A** which offers simple interest.

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