A man borrows रु 10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year?

Explanation

To solve the problem step by step, we will calculate the compound interest for each year, determine the amount paid back, and find the remaining unpaid amount after the second year.

### Step 1: Calculate the amount after the first year
Given:
- Principal (P) = रु 10,000
- Rate of interest (R) = 10%
- Time (T) = 1 year

The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

Substituting the values:
\[ A_1 = 10,000 \left(1 + \frac{10}{100}\right)^1 \]
\[ A_1 = 10,000 \left(1 + 0.10\right) \]
\[ A_1 = 10,000 \times 1.10 \]
\[ A_1 = 11,000 \text{ rupees} \]

### Step 2: Calculate the payment made at the end of the first year
The man pays back 20% of the amount after the first year:
\[ \text{Payment} = 20\% \text{ of } 11,000 \]
\[ \text{Payment} = \frac{20}{100} \times 11,000 \]
\[ \text{Payment} = 2,200 \text{ rupees} \]

### Step 3: Calculate the remaining unpaid amount after the first year
\[ \text{Unpaid Amount after Year 1} = A_1 - \text{Payment} \]
\[ \text{Unpaid Amount after Year 1} = 11,000 - 2,200 \]
\[ \text{Unpaid Amount after Year 1} = 8,800 \text{ rupees} \]

### Step 4: Calculate the amount after the second year
Now, the principal for the second year is the unpaid amount from the first year:
- New Principal (P) = 8,800 rupees

Using the same formula for the second year:
\[ A_2 = 8,800 \left(1 + \frac{10}{100}\right)^1 \]
\[ A_2 = 8,800 \times 1.10 \]
\[ A_2 = 9,680 \text{ rupees} \]

### Step 5: Calculate the payment made at the end of the second year
The man pays back 20% of the amount after the second year:
\[ \text{Payment} = 20\% \text{ of } 9,680 \]
\[ \text{Payment} = \frac{20}{100} \times 9,680 \]
\[ \text{Payment} = 1,936 \text{ rupees} \]

### Step 6: Calculate the remaining unpaid amount after the second year
\[ \text{Unpaid Amount after Year 2} = A_2 - \text{Payment} \]
\[ \text{Unpaid Amount after Year 2} = 9,680 - 1,936 \]
\[ \text{Unpaid Amount after Year 2} = 7,744 \text{ rupees} \]

### Final Answer
The amount left unpaid just after the second year is **रु 7,744**.

---