Gautam takes a loan of ₹ 16,000 for 2 years at 15% p.a. compound interest. He repays ₹ 9,000 at the end of first year. How much must he pay at the end of second year to clear the debt?

For 1st year:

P = ₹ 16,000

R = 15%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{16,000 \times 15 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{2,40,000}{100}\\[1em] = ₹ 2,400$

And

$\text{Amount = P + Interest}\\[1em] = ₹ 16,000 + 2,400\\[1em] = ₹ 18,400$

The amount at the end of first year, after making the repayment = ₹ 18,400 - ₹ 9,000

= ₹ 9,400

Hence, the amount at the end of first year, after making the repayment = ₹ 9,400

For 2nd year:

P = ₹ 9,400

R = 15%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{9,400 \times 15 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{141,000}{100}\\[1em] = ₹ 1,410$

And

$\text{Final amount = P + Interest}\\[1em] = ₹ 9,400 + 1,410\\[1em] = ₹ 10,810$

Hence, the amount to be paid at the end of the second year to clear the account = ₹ 10,810.