How can we derive the formula
 
Principle =  difference( in C.I.and S.I.)*100*100*100
                         R*R*(300+R)
 
                 for 3 years,where R=Rate of interest?

Asked by kideuttam | 26th Jan, 2015, 06:35: PM

Expert Answer:

W e space k n o w space C o m p o u n d space I n t e r e s t comma space C I equals P open parentheses 1 plus R over 100 close parentheses to the power of n minus P S i m p l e space I n t e r e s t comma space S I equals fraction numerator P cross times n cross times R over denominator 100 end fraction F o r space n equals 3 space y e a r s space C I equals P open parentheses 1 plus R over 100 close parentheses cubed minus P space space space equals P open parentheses 1 plus 3 R plus fraction numerator 3 R squared over denominator 10000 end fraction plus R cubed over 1000000 close parentheses minus P space space space equals P plus fraction numerator 3 P r over denominator 100 end fraction plus fraction numerator 3 P R squared over denominator 10000 end fraction plus fraction numerator P R cubed over denominator 1000000 end fraction minus P space space space equals fraction numerator 3 P R over denominator 100 end fraction plus fraction numerator 3 P R squared over denominator 10000 end fraction plus fraction numerator P R cubed over denominator 1000000 end fraction S I equals fraction numerator 3 P R over denominator 100 end fraction C I minus S I equals fraction numerator 3 P R over denominator 100 end fraction plus fraction numerator 3 P R squared over denominator 10000 end fraction plus fraction numerator P R cubed over denominator 1000000 end fraction minus fraction numerator 3 P R over denominator 100 end fraction rightwards double arrow C I minus S I equals fraction numerator 3 P R squared over denominator 10000 end fraction plus fraction numerator P r cubed over denominator 1000000 end fraction rightwards double arrow C I minus S I equals fraction numerator 300 P R squared plus P R cubed over denominator 1000000 end fraction rightwards double arrow fraction numerator open parentheses C I minus S I close parentheses cross times 100 cross times 100 cross times 100 over denominator 300 R squared plus R cubed end fraction equals P rightwards double arrow P equals fraction numerator open parentheses C I minus S I close parentheses cross times 100 cross times 100 cross times 100 over denominator left parenthesis 300 plus R right parenthesis R squared end fraction

Answered by Prasenjit Paul | 27th Jan, 2015, 10:17: AM