A person bought a refrigerator worth ₹22,800 with 12.5% interest compounded yearly. At the end of first year he paid ₹8,650 and at the end of second year ₹9,125. How much will he have to pay at the end of third year to clear the debt?

Correct Option (D)

The calculation for the outstanding debt at the end of the third year is as follows:

• Initial principal amount: ₹22,800.
• Interest for the first year: 12.5% of ₹22,800 = ₹2,850.
• Total debt at the end of the first year: ₹22,800 + ₹2,850 = ₹25,650.
• After the first payment of ₹8,650, the remaining principal for the second year is: ₹25,650 - ₹8,650 = ₹17,000.
• Interest for the second year: 12.5% of ₹17,000 = $\frac{12.5}{100}$ × 17,000 = ₹2,125.
• Total debt at the end of the second year: ₹17,000 + ₹2,125 = ₹19,125.
• After the second payment of ₹9,125, the remaining principal for the third year is: ₹19,125 - ₹9,125 = ₹10,000.
• Interest for the third year: 12.5% of ₹10,000 = $\frac{12.5}{100}$ × 10,000 = ₹1,250.
• The amount required to clear the debt at the end of the third year is: ₹10,000 + ₹1,250 = ₹11,250.

Incorrect Options:

Options (A) ₹9,990, (B) ₹10,000, and (C) ₹10,590 are incorrect because they do not reflect the accurate calculation of compound interest applied to the remaining principal after each payment. The correct methodology involves calculating interest on the outstanding balance at the beginning of each year and then subtracting the payments made, as demonstrated in the correct option's explanation.