Kruti took a loan at simple interest at 6% in the first year with an increase of `0.5%` in each subsequent year. She paid Rs 3375 as interest after 4 years. How much loan did she take?

Options

A. Rs 12500
B. Rs 15800
C. Rs 33250
D. Rs 30,000

Answer

To find out how much loan Kruti took, we will follow these steps:

### Step 1: Understand the interest rates for each year
- In the first year, the interest rate is 6%.
- In the second year, the interest rate increases by 0.5%, making it 6.5%.
- In the third year, the interest rate increases again by 0.5%, making it 7%.
- In the fourth year, the interest rate increases once more by 0.5%, making it 7.5%.

### Step 2: Calculate the total interest paid over 4 years
The total interest paid after 4 years is given as Rs 3375. We will calculate the interest for each year based on the principal amount (P).

### Step 3: Write the formula for interest for each year
- Interest for the first year = \( P \times \frac{6}{100} \)
- Interest for the second year = \( P \times \frac{6.5}{100} \)
- Interest for the third year = \( P \times \frac{7}{100} \)
- Interest for the fourth year = \( P \times \frac{7.5}{100} \)

### Step 4: Sum up the interest for all four years
The total interest for 4 years can be expressed as:
\[ \text{Total Interest} = P \times \left( \frac{6}{100} + \frac{6.5}{100} + \frac{7}{100} + \frac{7.5}{100} \right) \]

### Step 5: Calculate the sum of the interest rates
Calculating the sum:
\[ \frac{6 + 6.5 + 7 + 7.5}{100} = \frac{27}{100} \]

### Step 6: Set up the equation
Now we can set up the equation based on the total interest paid:
\[ P \times \frac{27}{100} = 3375 \]

### Step 7: Solve for P
To find P, we can rearrange the equation:
\[ P = 3375 \times \frac{100}{27} \]

### Step 8: Calculate P
Calculating the value:
\[ P = 3375 \times \frac{100}{27} = 3375 \div 27 \times 100 \]
Calculating \( 3375 \div 27 = 125 \):
\[ P = 125 \times 100 = 12500 \]

### Conclusion
The principal amount (loan) that Kruti took is Rs 12,500.

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