The compound interest on a certain sum in 2.5 years at 10% p.a., interest compounded yearly, is 1,623. The sum is:

given CI= 1623, T= 2.5year, r= 10% after 2 years rate of interest count in half-yearly then will be r= 5% Let P=x then A= CI-P=1623-x So now 1623-x = x [1+10/100] ² [1+5/100] 1623-x = x [121/100] [21/20] 1623-x =x [2541/2000] (1623×2000-2000x) =2541x 541x=1623×2000 x= 1623×2000/541 x=6000rs short method –r= 10%=1/10 then      P             A                10           11           first year                10           11           second year                20           21           After 2year rate of interest count will be half-yearly then r=5% =1/20                2000      2541 CI=A-P=2541-2000=541                but ATQ compound interest is 1623 So 541=1623 1=1623/541 Then P 2000=1623×2000/541 P= 6000rs