A man borrows 6000 at 5% interest, on reducing balance, at the start of the year. If he repays 1200 at the end of each year, find the amount of loan outstanding, (in ), at the beginning of the third year.

Options

A. 3162.75
B. `4155.00`
C. `4155.00`
D. `5100.00`

Answer

To find the amount of loan outstanding at the beginning of the third year, we will follow these steps:

### Step 1: Calculate the interest for the first year
The principal amount borrowed is Rs 6000, and the interest rate is 5%.

\[ \text{Interest for the first year} = \text{Principal} \times \text{Rate} = 6000 \times \frac{5}{100} = 6000 \times 0.05 = 300 \]

### Step 2: Calculate the total amount due at the end of the first year
At the end of the first year, the total amount due will be the principal plus the interest.

\[ \text{Total amount due} = \text{Principal} + \text{Interest} = 6000 + 300 = 6300 \]

### Step 3: Subtract the repayment made at the end of the first year
The man repays Rs 1200 at the end of the first year.

\[ \text{Outstanding loan after repayment} = \text{Total amount due} - \text{Repayment} = 6300 - 1200 = 5100 \]

### Step 4: Calculate the interest for the second year
Now, the outstanding loan is Rs 5100. We will calculate the interest for the second year.

\[ \text{Interest for the second year} = 5100 \times 0.05 = 255 \]

### Step 5: Calculate the total amount due at the end of the second year
At the end of the second year, the total amount due will be the outstanding loan plus the interest.

\[ \text{Total amount due} = \text{Outstanding loan} + \text{Interest} = 5100 + 255 = 5355 \]

### Step 6: Subtract the repayment made at the end of the second year
The man again repays Rs 1200 at the end of the second year.

\[ \text{Outstanding loan after repayment} = \text{Total amount due} - \text{Repayment} = 5355 - 1200 = 4155 \]

### Conclusion
The amount of loan outstanding at the beginning of the third year is Rs 4155.

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