Ranbir borrows  Rs20,000 at 12% per annum compound interest. If he repays  Rs8400 at the end of the first year and  Rs9680 at the end of the second year. Find the amount of loan outstanding at the beginning of the third year.

The correct answer is: Rs 6000

Complete step by step solution:
Money borrowed by Ranbir at 12% compound interest, that is  = Rs 20000
For first year,
We know that compound interest = Total amount - principal amount that is, CI = A - P …(i)
Here we have …(ii)
Here, we have T = 1 years, P = 20000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get 

 Rs
Thus total amount after 1 year = 20000+2400=22400 Rupees.
Money repaid = Rs 8400
∴ Balance = 22400 - 8400 = 14000 Rupees.
For second year,
Here, we have T = 1 years, P = 14000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get 
 Rs
Thus total amount after 1 year = 14000+1680=15680 Rupees.
Money paid at the end of second year by Ranbir = Rs 9680
∴ Loan at the beginning of third year = 15680 - 9680 = Rs 6000