A person bought a refrigerator worth Rs. 22,800 with 12.5% interest compounded yearly. At the end of first year he paid Rs. 8,650 and at the end of second year Rs. 9,125. How much will he have to pay at the end of third year to clear the debt? (UPSC 2017)

Step 1: Calculate the amount after one year with interest.

The formula for compound interest is A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

In this case, P = Rs. 22,800, r = 12.5% or 0.125, n = 1 (since interest is compounded yearly), and t = 1 year.

So, A = 22800(1 + 0.125/1)^(1*1) = Rs. 25,650

Step 2: Subtract the payment made at the end of the first year.

The person paid Rs. 8,650 at the end of the first year, so subtract this from the amount calculated in step 1: 25,650 - 8,650 = Rs. 17,000. This is the new principal amount for the second year.

Step 3: Calculate the amount after the second year with interest.

Using the same formula as in step 1, but with the new principal amount (P = Rs. 17,000), we get: A = 17000(1 + 0.125/1)^(1*1) = Rs. 19,125

Step 4: Subtract the payment made at the end of the second year.

The person paid Rs. 9,125 at the end of the second year, so subtract this from the amount calculated in step 3: 19,125 - 9,125 = Rs. 10,000. This is the new principal amount for the third year.

Step 5: Calculate the amount after the third year with interest.

Using the same formula as in step 1, but with the new principal amount (P = Rs. 10,000), we get: A = 10000(1 + 0.125/1)^(1*1) = Rs. 11,250

So, the person will have to pay Rs. 11,250 at the end of the third year to clear the debt.