Peter borrows ₹ 12,000 for 2 years at 10% p.a. compound interest. He repays ₹ 8,000 at the end of first year. Find:

(i) the amount at the end of first year, before making the repayment.

(ii) the amount at the end of first year, after making the repayment.

(iii) the principal for the second year.

(iv) the amount to be paid at the end of the second year to clear the account.

For 1st year:

P = ₹ 12,000

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{12,000 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{1,20,000}{100}\\[1em] = ₹ 1,200$

And

$\text{Amount = P + Interest}\\[1em] = ₹ 12,000 + 1,200\\[1em] = ₹ 13,200$

Hence, the amount at the end of first year, before making the repayment = ₹ 13,200

(ii) The amount at the end of first year, after making the repayment = ₹ 13,200 - ₹ 8,000

= ₹ 5,200

Hence, the amount at the end of first year, after making the repayment = ₹ 5,200

(iii) So, the principal amount for second year = ₹ 5,200

(iv) For 2nd year:

P = ₹ 5,200

R = 10%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{5,200 \times 10 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{52,000}{100}\\[1em] = ₹ 520$

And

$\text{Final amount = P + Interest}\\[1em] = ₹ 5,200 + 520\\[1em] = ₹ 5,720$

Hence, the amount to be paid at the end of the second year to clear the account = ₹ 5,720.