Kanika took a loan of Rs. 10,000 for 2 years on compound interest at the rate of 5% per annum, interest being compounded annually. How much money would she have saved if she had taken the loan on simple interest?

Options

A. Rs. 1,025
B. Rs. 1,000
C. Rs. 25
D. Rs. 400

Answer

To solve the problem, we need to calculate the amount of money Kanika would have saved if she had taken the loan on simple interest instead of compound interest. We will first calculate the total amount paid under both interest schemes and then find the difference.

### Step 1: Calculate the amount with Compound Interest (CI)

The formula for compound interest is:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \(A\) = Total amount after time \(n\)
- \(P\) = Principal amount (initial loan)
- \(r\) = Rate of interest per annum
- \(n\) = Number of years

Given:
- \(P = 10,000\)
- \(r = 5\%\)
- \(n = 2\)

Substituting the values into the formula:

\[ A = 10000 \left(1 + \frac{5}{100}\right)^2 \]

Calculating inside the parentheses:

\[ A = 10000 \left(1 + 0.05\right)^2 = 10000 \left(1.05\right)^2 \]

Calculating \(1.05^2\):

\[ 1.05^2 = 1.1025 \]

Now substituting back:

\[ A = 10000 \times 1.1025 = 11025 \]

### Step 2: Calculate the amount with Simple Interest (SI)

The formula for simple interest is:

\[ A = P + SI \]

Where:

\[ SI = \frac{P \times r \times n}{100} \]

Calculating the simple interest:

\[ SI = \frac{10000 \times 5 \times 2}{100} = \frac{100000}{100} = 1000 \]

Now substituting back to find the total amount:

\[ A = 10000 + 1000 = 11000 \]

### Step 3: Calculate the difference between Compound Interest and Simple Interest

Now, we will find the difference between the total amounts calculated:

\[ \text{Difference} = A_{CI} - A_{SI} = 11025 - 11000 = 25 \]

### Conclusion

Kanika would have saved Rs. 25 if she had taken the loan on simple interest instead of compound interest.

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