Question

a man borrows 10000 Rupees at 10% compound interest compounded yearly at the end of each year he pays back 20% of the amount for each year how much money is a left and paid just after 2nd year

Answer 1

R = P (1+r)^1  at the end of one year.     20% of R  is paid back.   I assume 20 % of (money with compound interest) at the end of the year is paid back. 

Remaining amount is : R - 20% R = 80% R = 0.80 P (1+r) 
     = 0.80 * 10000 * (1+10/100)      =    Rs 8000 * 1.10  = Rs 8800

For 2nd year R = 8800 (1+r)^1  = Rs 8800 * 1.10 = Rs 9680
Amount paid back at end of 2nd year is : 20% * Rs 9680
Amount left unpaid =  Rs 9680 * 80 % = Rs 9680 * 0.80  = Rs 7744