Question

ashook borrowed rs.12000 at some rate percent compound interest.after a year he paid back rs.4000.if compound interest for second year be rs.920, find:1)the rate of interest charged.
2)the amount of debt at the end of the second year.

Answer 1

P = Rs 12,000
After one year the sum accumulated with compound interest
             = P (1 +r/100) = 12,000+120 r
Rs 4,000 is returned.
Remaining amount = 8,000 + 120 r  at the end of 1st year.

Sum accumulated at the end of 2nd year = (8,000+120r)(1 + r/100)
         = 8,000 + 200 r + 1.2 r²
I am not sure if the compound interest for the second year is to be taken as :
         8,000 + 200 r + 1.2 r² - (8,000 + 120 r) = 1.2 r² + 80 r
 
  hence,  1.2 r² + 80 r = 920    => 3 r² + 200 r - 2300 = 0
                     3 r² +230 r - 30 r - 2300 = 0
                 (3 r + 230) r - 10 (3 r + 230) = 0
                    r = 10 %  as r is positive we ignore the negative root.
  
accumulated sum at the end of 2nd year = 8,000 + 200 * 10 + 1.2 * 10²
     = Rs 10,120