The interest charged on a certain sum is Rs.720 for one year and Rs.1497.60 for two years. Find whether the interest is simple or compound. Also calculate the rate per cent and the sum. 

Asked by pratyakshajha.12 | 26th May, 2015, 08:38: AM

Expert Answer:

L e t space t h e space p r i n c i p a l space b e space apostrophe P apostrophe space a n d space i n t e r e s t space b e space apostrophe r % apostrophe. N o w comma space f o r space t h e space f i r s t space y e a r space i n t e r e s t space equals space R s space 720 F o r space t h e space s e c o n d space y e a r space i n t e r e s t space equals space R s space 1497.6 D i f f e r e n c e space b e t w e e n space t h e space i n t e r e s t space f o r space t w o space y e a r s space equals space 1497.6 minus 720 space equals space R s. space 777.60 S i n c e space t h e space i n t e r e s t space i s space d i f f e r e n t space i n space e a c h space o f space t h e space y e a r s comma space t h e r e f o r e space t h e space i n t e r e s t space i s space c o m p o u n d space i n t e r e s t comma space sin c e i n space a space si m p l e space i n t e r e s t comma space i n t e r e s t s space w i l l space b e space s a m e space i n space e a c h space y e a r.  I n space t h e space f i r s t space y e a r comma fraction numerator P cross times r cross times 1 over denominator 100 end fraction equals 720 P r space equals space 72000......... left parenthesis i right parenthesis  I n space t h e space s e c o n d space y e a r comma P open parentheses 1 plus r over 100 close parentheses squared equals P plus 1497.60 rightwards double arrow P open parentheses 1 plus fraction numerator 2 r over denominator 100 end fraction plus r squared over 100 squared close parentheses equals P plus 1497.60 rightwards double arrow P plus fraction numerator 2 P r over denominator 100 end fraction plus fraction numerator P r squared over denominator 100 squared end fraction equals P plus 1497.60 rightwards double arrow fraction numerator 2 P r over denominator 100 end fraction plus fraction numerator P r squared over denominator 100 squared end fraction equals 1497.60 rightwards double arrow fraction numerator 2 cross times 72000 over denominator 100 end fraction plus fraction numerator 72000 cross times r over denominator 10000 end fraction equals 1497.60 rightwards double arrow 1440 plus fraction numerator 72 r over denominator 10 end fraction equals 1497.60 rightwards double arrow fraction numerator 72 r over denominator 10 end fraction equals 1497.60 minus 1440 rightwards double arrow fraction numerator 72 r over denominator 10 end fraction equals 57.6 rightwards double arrow r equals 576 over 72 therefore r equals 8 %  F r o m space left parenthesis i right parenthesis P cross times r equals 72000 rightwards double arrow P equals 72000 over 8 therefore P equals R s. space 8000 S u m space equals space R s. space 8000 R a t e space o f space i n t e r e s t space equals space 8 %

Answered by Prasenjit Paul | 26th May, 2015, 09:58: AM

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