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?

The correct option is ₹ 11,250.

Let us break down the calculations step-by-step to understand how the debt is cleared over the three years at an interest rate of 12.5% compounded yearly.

Step 1: Calculate the outstanding amount at the end of the first year (before the first payment)
The initial principal amount (worth of the refrigerator) is:
Principal, $P_1=\text{₹}\mathrm{22,800}$
The annual rate of interest is:
$R=12.5\%$
Interest accrued at the end of the first year is:
$I_1=P_1\times \frac{R}{100}=\mathrm{22,800}\times \frac{12.5}{100}=\mathrm{22,800}\times 0.125=\text{₹}\mathrm{2,850}$
Total amount due at the end of the first year before payment is:
$A_1=P_1+I_1=\mathrm{22,800}+\mathrm{2,850}=\text{₹}\mathrm{25,650}$

Step 2: Calculate the remaining principal for the second year after the first payment
The person pays ₹ 8,650 at the end of the first year.
Remaining principal for the second year is:
$P_2=A_1-\mathrm{8,650}=\mathrm{25,650}-\mathrm{8,650}=\text{₹}\mathrm{17,000}$

Step 3: Calculate the outstanding amount at the end of the second year (before the second payment)
Interest accrued on the remaining principal during the second year is:
$I_2=P_2\times 0.125=\mathrm{17,000}\times 0.125=\text{₹}\mathrm{2,125}$
Total amount due at the end of the second year before payment is:
$A_2=P_2+I_2=\mathrm{17,000}+\mathrm{2,125}=\text{₹}\mathrm{19,125}$

Step 4: Calculate the remaining principal for the third year after the second payment
The person pays ₹ 9,125 at the end of the second year.
Remaining principal for the third year is:
$P_3=A_2-\mathrm{9,125}=\mathrm{19,125}-\mathrm{9,125}=\text{₹}\mathrm{10,000}$

Step 5: Calculate the final payment needed at the end of the third year to clear the debt
Interest accrued on the remaining principal during the third year is:
$I_3=P_3\times 0.125=\mathrm{10,000}\times 0.125=\text{₹}\mathrm{1,250}$
Total amount due at the end of the third year to completely clear the debt is:
$A_3=P_3+I_3=\mathrm{10,000}+\mathrm{1,250}=\text{₹}\mathrm{11,250}$

Therefore, the amount he will have to pay at the end of the third year to clear the debt is ₹ 11,250.