Question

Ashok borrowed Rs.12000 at some rate of interest. After a year,he paid back Rs.4000. If compound interest for second year be Rs.920, Find the rate of int and the amount of debt at the end of the second year.

Answer 1

Principal (i) = 12000  Rs
After 1 year he paid back Rs 4000
Let the rate of interest be r
Hence the principle after 1 year 12000(1+r/100)-4000
Now it is given that C.I for 2nd year = 920
Hence {12000(1+r/100)-4000}(1+r/100)
= {12000(1+r/100)-4000 +920}
=> (1+r/100)= {12000(1+r/100)-4000 +920}/{12000(1+r/100)-4000}
 
=> (1+r/100)= {8920+120r}/{8000+120r}
 
=> r/100=   {8920+120r}/{8000+120r}   - 1
 
=> r/100 = 920/8000+120r
 
=> 120r2+8000r-92000 = 0
 
=> 3r2+200r-2300=0
               
=> 3r2 -30r+230r-2300=0
 
=> 3r(r-10)230(r-10)=0
 
=> (3r+230)(r-10)=0
 
Since rate cannot be negative
Hence r = 10
Therefore rate of interest =10%

2.            Now initial principle = 12000
C.I for 1st year = 12000(1+10/100)-12000
                           =13200-12000=1200
C.I. for 2nd year =920
Hence sum of principle and interest of both years=12000+1200+920=14120
But he paid back 4000
Hence amount of debt at the end of 2nd year = 14120-4000= 10120 Rs.

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