On a certain sum of money, the difference between the compound interest for a year, payable half yearly, and the simple interest for a year is Rs 16. Find the sum lent out, if the rate of interest in both cases is 8 % .
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let sum be Rs.x, time(t)=1 year for si and 2 half years for ci, r=8% for si and 8/2=4% for ci.
si= x*8*1/100= Rs.2x/25
ci= x(1+ 4/100)^2-x
= x*(26/25)^2-x
=x*676/625-x
=676-625x/625
=Rs.51x/625
subtracting si from ci
51x/625 - 2x/25
=51x-50x/625
=1x/625
difference given= rs.16
therefore 1x/625=16
=>x=625*16
=>x=10000
sum=Rs.10000
si= x*8*1/100= Rs.2x/25
ci= x(1+ 4/100)^2-x
= x*(26/25)^2-x
=x*676/625-x
=676-625x/625
=Rs.51x/625
subtracting si from ci
51x/625 - 2x/25
=51x-50x/625
=1x/625
difference given= rs.16
therefore 1x/625=16
=>x=625*16
=>x=10000
sum=Rs.10000
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