If interest is added at the end of half-year to the principal invested, find the amount to which rs.240 increases, at 5% p.a. by the end of the first year .

Asked by rickykumar00001 | 1st Jan, 2016, 04:44: PM

Expert Answer:

L e t space apostrophe P apostrophe space b e space t h e space p r i n c i p a l space i n v e s t e d. S i m p l e space i n t e r e s t space a t space t h e space e n d space o f space h a l f minus y e a r space a t space 5 percent sign space i n t e r e s t space r a t e equals fraction numerator P cross times 6 cross times 5 over denominator 12 cross times 100 end fraction equals fraction numerator 5 P over denominator 200 end fraction equals P over 40 T h u s space t h e space a m o u n t space a f t e r space h a l f space y e a r equals P plus P over 40 equals P open parentheses 1 plus 1 over 40 close parentheses equals fraction numerator 41 P over denominator 40 end fraction P r i n c i p a l space f o r space t h e space n e x t space h a l f minus y e a r equals fraction numerator 41 P over denominator 40 end fraction S i m p l e space i n t e r e s t space a t space t h e space e n d space o f space t h e space y e a r space a f t e r space 6 space m o n t h s comma space a t space 5 percent sign space i n t e r e s t space r a t e equals fraction numerator fraction numerator 41 P over denominator 40 end fraction cross times 6 cross times 5 over denominator 12 cross times 100 end fraction equals fraction numerator 41 P cross times 1 cross times 5 over denominator 40 cross times 2 cross times 100 end fraction equals fraction numerator 41 P over denominator 40 cross times 40 end fraction T h u s space t h e space t o t a l space a m o u n t space a t space t h e space e n d space o f space t h e space y e a r equals fraction numerator 41 P over denominator 40 end fraction plus fraction numerator 41 P over denominator 40 cross times 40 end fraction equals fraction numerator 41 P over denominator 40 end fraction open parentheses 1 plus 1 over 40 close parentheses equals fraction numerator 41 P over denominator 40 end fraction cross times 41 over 40 G i v e n space t h a t space t o t a l space a m o u n t equals P plus R s.240 rightwards double arrow fraction numerator 41 P over denominator 40 end fraction cross times 41 over 40 equals P plus 240 rightwards double arrow fraction numerator 41 squared P over denominator 40 squared end fraction equals P plus 240 rightwards double arrow fraction numerator 41 squared P over denominator 40 squared end fraction minus P equals 240 rightwards double arrow fraction numerator 41 squared P minus 40 squared P over denominator 40 squared end fraction equals 240 rightwards double arrow P fraction numerator open parentheses 41 squared minus 40 squared close parentheses over denominator 40 squared end fraction equals 240 rightwards double arrow P fraction numerator open parentheses 1681 minus 1600 close parentheses over denominator 1600 end fraction equals 240 rightwards double arrow P 81 over 1600 equals 240 rightwards double arrow P equals fraction numerator 240 cross times 1600 over denominator 81 end fraction rightwards double arrow P equals 384000 over 81 rightwards double arrow P equals R s.4740.75

Answered by Vimala Ramamurthy | 2nd Jan, 2016, 10:31: AM