Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 11A - Compound Interest
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Page 1 ( Q u e s t i o n 1 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 2 5 0 0 f o r 2 y e a r s a t 1 0 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 0 % p e r a n n u m T i m e = 2 y e a r s = 4 h a l f - y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 ( Q u e s t i o n 2 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 1 5 6 2 5 f o r 3 y e a r s a t 1 2 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 2 % p e r a n n u m T i m e = 3 y e a r s O r i g i n a l p r i n c i p l e = R s 1 5 6 2 5 Page 2 ( Q u e s t i o n 1 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 2 5 0 0 f o r 2 y e a r s a t 1 0 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 0 % p e r a n n u m T i m e = 2 y e a r s = 4 h a l f - y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 ( Q u e s t i o n 2 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 1 5 6 2 5 f o r 3 y e a r s a t 1 2 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 2 % p e r a n n u m T i m e = 3 y e a r s O r i g i n a l p r i n c i p l e = R s 1 5 6 2 5 A m o u n t a t t h e e n d o f t h e t h i r d y e a r = R s ( 1 9 6 0 0 + 2 3 5 2 ) = R s 2 1 9 5 2 ? C o m p o u n d i n t e r e s t = R s ( 2 1 9 5 2 – 1 5 6 2 5 ) = R s 6 3 2 7 . ( Q u e s t i o n 3 ) F i n d t h e d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d t h e c o m p o u n d i n t e r e s t o n R s 5 0 0 0 f o r 2 y e a r s a t 9 % p e r a n n u m . Page 3 ( Q u e s t i o n 1 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 2 5 0 0 f o r 2 y e a r s a t 1 0 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 0 % p e r a n n u m T i m e = 2 y e a r s = 4 h a l f - y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 ( Q u e s t i o n 2 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 1 5 6 2 5 f o r 3 y e a r s a t 1 2 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 2 % p e r a n n u m T i m e = 3 y e a r s O r i g i n a l p r i n c i p l e = R s 1 5 6 2 5 A m o u n t a t t h e e n d o f t h e t h i r d y e a r = R s ( 1 9 6 0 0 + 2 3 5 2 ) = R s 2 1 9 5 2 ? C o m p o u n d i n t e r e s t = R s ( 2 1 9 5 2 – 1 5 6 2 5 ) = R s 6 3 2 7 . ( Q u e s t i o n 3 ) F i n d t h e d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d t h e c o m p o u n d i n t e r e s t o n R s 5 0 0 0 f o r 2 y e a r s a t 9 % p e r a n n u m . A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 5 4 5 0 + 4 9 0 . 5 ) = R s 5 9 4 0 . 5 ? C o m p o u n d i n t e r e s t = R s ( 5 9 4 0 . 5 – 5 0 0 0 ) = R s 9 4 0 . 5 . N o w , d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d c o m p o u n d i n t e r e s t = R s ( 9 4 0 . 5 – 9 0 0 ) = R s 4 0 . 5 ( Q u e s t i o n 4 ) R a t n a o b t a i n e d a l o a n o f R s 2 5 0 0 0 f r o m t h e S y n d i c a t e B a n k t o r e n o v a t e h e r h o u s e . I f t h e r a t e o f i n t e r e s t i s 8 % p e r a n n u m , w h a t a m o u n t w i l l s h e h a v e t o p a y t o t h e b l a n k a f t e r 2 y e a r s t o d i s c h a r g e h e r d e b t ? S o l u t i o n : R a t e o f i n t e r e s t = 8 % p e r a n n u m T i m e = 2 y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 0 Page 4 ( Q u e s t i o n 1 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 2 5 0 0 f o r 2 y e a r s a t 1 0 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 0 % p e r a n n u m T i m e = 2 y e a r s = 4 h a l f - y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 ( Q u e s t i o n 2 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 1 5 6 2 5 f o r 3 y e a r s a t 1 2 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 2 % p e r a n n u m T i m e = 3 y e a r s O r i g i n a l p r i n c i p l e = R s 1 5 6 2 5 A m o u n t a t t h e e n d o f t h e t h i r d y e a r = R s ( 1 9 6 0 0 + 2 3 5 2 ) = R s 2 1 9 5 2 ? C o m p o u n d i n t e r e s t = R s ( 2 1 9 5 2 – 1 5 6 2 5 ) = R s 6 3 2 7 . ( Q u e s t i o n 3 ) F i n d t h e d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d t h e c o m p o u n d i n t e r e s t o n R s 5 0 0 0 f o r 2 y e a r s a t 9 % p e r a n n u m . A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 5 4 5 0 + 4 9 0 . 5 ) = R s 5 9 4 0 . 5 ? C o m p o u n d i n t e r e s t = R s ( 5 9 4 0 . 5 – 5 0 0 0 ) = R s 9 4 0 . 5 . N o w , d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d c o m p o u n d i n t e r e s t = R s ( 9 4 0 . 5 – 9 0 0 ) = R s 4 0 . 5 ( Q u e s t i o n 4 ) R a t n a o b t a i n e d a l o a n o f R s 2 5 0 0 0 f r o m t h e S y n d i c a t e B a n k t o r e n o v a t e h e r h o u s e . I f t h e r a t e o f i n t e r e s t i s 8 % p e r a n n u m , w h a t a m o u n t w i l l s h e h a v e t o p a y t o t h e b l a n k a f t e r 2 y e a r s t o d i s c h a r g e h e r d e b t ? S o l u t i o n : R a t e o f i n t e r e s t = 8 % p e r a n n u m T i m e = 2 y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 0 A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 2 7 0 0 0 + 2 1 6 0 ) = R s 2 9 1 6 0 T h e r e f o r e , s h e h a s t o p a y R s 2 9 1 6 0 t o t h e b l a n k a f t e r 2 y e a r s t o d i s c h a r g e h e r d e b t ( Q u e s t i o n 5 ) H a r p r e e t b o r r o w e d R s 2 0 0 0 0 f r o m h e r f r i e n d a t 1 2 % p e r a n n u m s i m p l e i n t e r e s t . S h e l e n t i t t o A l a m a t t h e s a m e r a t e b u t c o m p o u n d e d a n n u a l l y . F i n d h e r g a i n a f t e r 2 y e a r s . A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 2 2 4 0 0 + 2 6 8 8 ) = R s 2 5 0 8 8 ? C o m p o u n d i n t e r e s t = R s ( 2 5 0 8 8 – 2 0 0 0 0 ) = R s 5 0 8 8 N o w , C I – S I = R s ( 5 0 8 8 – 4 8 0 0 ) = R s 2 8 8 Page 5 ( Q u e s t i o n 1 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 2 5 0 0 f o r 2 y e a r s a t 1 0 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 0 % p e r a n n u m T i m e = 2 y e a r s = 4 h a l f - y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 ( Q u e s t i o n 2 ) F i n d t h e a m o u n t a n d t h e c o m p o u n d i n t e r e s t o n R s 1 5 6 2 5 f o r 3 y e a r s a t 1 2 % p e r a n n u m , c o m p o u n d e d a n n u a l l y . S o l u t i o n : R a t e o f i n t e r e s t = 1 2 % p e r a n n u m T i m e = 3 y e a r s O r i g i n a l p r i n c i p l e = R s 1 5 6 2 5 A m o u n t a t t h e e n d o f t h e t h i r d y e a r = R s ( 1 9 6 0 0 + 2 3 5 2 ) = R s 2 1 9 5 2 ? C o m p o u n d i n t e r e s t = R s ( 2 1 9 5 2 – 1 5 6 2 5 ) = R s 6 3 2 7 . ( Q u e s t i o n 3 ) F i n d t h e d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d t h e c o m p o u n d i n t e r e s t o n R s 5 0 0 0 f o r 2 y e a r s a t 9 % p e r a n n u m . A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 5 4 5 0 + 4 9 0 . 5 ) = R s 5 9 4 0 . 5 ? C o m p o u n d i n t e r e s t = R s ( 5 9 4 0 . 5 – 5 0 0 0 ) = R s 9 4 0 . 5 . N o w , d i f f e r e n c e b e t w e e n t h e s i m p l e i n t e r e s t a n d c o m p o u n d i n t e r e s t = R s ( 9 4 0 . 5 – 9 0 0 ) = R s 4 0 . 5 ( Q u e s t i o n 4 ) R a t n a o b t a i n e d a l o a n o f R s 2 5 0 0 0 f r o m t h e S y n d i c a t e B a n k t o r e n o v a t e h e r h o u s e . I f t h e r a t e o f i n t e r e s t i s 8 % p e r a n n u m , w h a t a m o u n t w i l l s h e h a v e t o p a y t o t h e b l a n k a f t e r 2 y e a r s t o d i s c h a r g e h e r d e b t ? S o l u t i o n : R a t e o f i n t e r e s t = 8 % p e r a n n u m T i m e = 2 y e a r s O r i g i n a l p r i n c i p l e = R s 2 5 0 0 0 A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 2 7 0 0 0 + 2 1 6 0 ) = R s 2 9 1 6 0 T h e r e f o r e , s h e h a s t o p a y R s 2 9 1 6 0 t o t h e b l a n k a f t e r 2 y e a r s t o d i s c h a r g e h e r d e b t ( Q u e s t i o n 5 ) H a r p r e e t b o r r o w e d R s 2 0 0 0 0 f r o m h e r f r i e n d a t 1 2 % p e r a n n u m s i m p l e i n t e r e s t . S h e l e n t i t t o A l a m a t t h e s a m e r a t e b u t c o m p o u n d e d a n n u a l l y . F i n d h e r g a i n a f t e r 2 y e a r s . A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 2 2 4 0 0 + 2 6 8 8 ) = R s 2 5 0 8 8 ? C o m p o u n d i n t e r e s t = R s ( 2 5 0 8 8 – 2 0 0 0 0 ) = R s 5 0 8 8 N o w , C I – S I = R s ( 5 0 8 8 – 4 8 0 0 ) = R s 2 8 8 ( Q u e s t i o n 6 ) M a n o j d e p o s i t e d a s u m o f R s 6 4 0 0 0 i n a p o s t o f f i c e f o r 3 y e a r s , c o m p o u n d e d a n n u a l l y a t 7 ( 1 / 2 ) % p e r a n n u m . W h a t a m o u n t w i l l h e g e t o n m a t u r i t y ? A m o u n t a t t h e e n d o f t h e s e c o n d y e a r = R s ( 6 8 8 0 0 + 5 1 6 0 ) = R s 7 3 9 6 0 P r i n c i p l e f o r t h e t h i r d y e a r = R s 7 3 9 6 0 A m o u n t a t t h e e n d o f t h e t h i r d y e a r = R s ( 7 3 9 6 0 + 5 5 4 7 ) = R s 7 9 5 0 7 T h e r e f o r e , M a n o j w i l l g e t R s 7 9 5 0 7 o n m a t u r i t y . ( Q u e s t i o n 7 ) D i v a k a r a n d e p o s i t e d a s u m o f R s 6 2 5 0 i n t h e A l l a h a b a d b a n k f o r 1 y e a r , c o m p o u n d e d h a l f - y e a r l y a t 8 % p e r a n n u m . F i n d t h e c o m p o u n d i n t e r e s t h e g e t s . S o l u t i o n : R a t e o f i n t e r e s t = 8 % p e r a n n u m = 4 % f o r h a l f y e a r T i m e = 1 y e a r = 2 h a l f y e a r O r i g i n a l p r i n c i p l e = R s 6 2 5 0 . P r i n c i p l e f o r t h e f i r s t h a l f y e a r = R s 6 2 5 0Read More
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