Sameer borrowed 17500 Rs. from Divyaraj on compound interest annually at the rate of 20% per annum, if he paid 5000 Rs. at the end of every year to Divyaraj then find how much amount Sameer have to pay at the end of fourth year for complete his debt?

Options

A. A)14168
B. B)14648
C. C)14848
D. D)14448

Answer

To solve the problem step by step, we will calculate how much Sameer owes at the end of each year, considering the compound interest and the payments he makes.

### Step 1: Calculate the amount after the first year
Sameer borrowed Rs. 17,500 at an interest rate of 20% per annum.

The formula for compound interest is:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the amount after time \( n \)
- \( P \) is the principal amount (initial amount)
- \( r \) is the rate of interest (as a decimal)
- \( n \) is the number of years

For the first year:
- \( P = 17500 \)
- \( r = 0.20 \)
- \( n = 1 \)

Calculating the amount after the first year:
\[ A_1 = 17500 \times (1 + 0.20)^1 = 17500 \times 1.2 = 21000 \]

After paying Rs. 5000 at the end of the first year:
Remaining amount after Year 1:
\[ \text{Remaining} = 21000 - 5000 = 16000 \]

### Step 2: Calculate the amount after the second year
Now, we will calculate the amount for the second year using the remaining amount.

For the second year:
- \( P = 16000 \)

Calculating the amount after the second year:
\[ A_2 = 16000 \times (1 + 0.20)^1 = 16000 \times 1.2 = 19200 \]

After paying Rs. 5000 at the end of the second year:
Remaining amount after Year 2:
\[ \text{Remaining} = 19200 - 5000 = 14200 \]

### Step 3: Calculate the amount after the third year
Now, we will calculate the amount for the third year using the remaining amount.

For the third year:
- \( P = 14200 \)

Calculating the amount after the third year:
\[ A_3 = 14200 \times (1 + 0.20)^1 = 14200 \times 1.2 = 17040 \]

After paying Rs. 5000 at the end of the third year:
Remaining amount after Year 3:
\[ \text{Remaining} = 17040 - 5000 = 12040 \]

### Step 4: Calculate the amount after the fourth year
Now, we will calculate the amount for the fourth year using the remaining amount.

For the fourth year:
- \( P = 12040 \)

Calculating the amount after the fourth year:
\[ A_4 = 12040 \times (1 + 0.20)^1 = 12040 \times 1.2 = 14448 \]

### Conclusion
At the end of the fourth year, Sameer has to pay Rs. 14,448 to clear his debt.