The simple interest on a sum of money for 5 years at 7% p.a. is ?800more than the simple interest on the same sum of three years at 9%per annum. Find the original sum of money.

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Solution

Dear Student,

$L e t P b e t h e o r i g i n a l a m o u n t o r p r i n c i p a l . W e k n o w, S i m p l e I n t e r e s t (S I) = \frac{P \times R \times T}{100} C a s e 1 : R a t e o f i n t e r e s t, R_{1} = 7 % p a . a T i m e, T_{1} = 5 y e a r s S I_{1} = \frac{P \times R_{1} \times T_{1}}{100} = \frac{P \times 7 \times 5}{100} = \frac{35 P}{100} C a s e 2 : R a t e o f i n t e r e s t, R_{2} = 9 % p . a T i m e, T_{2} = 3 y e a r s S I_{2} = \frac{P \times R_{2} \times T_{2}}{100} = \frac{P \times 9 \times 3}{100} = \frac{27 P}{100} A c c o r d i n g t o t h e q u e s t i o n : S I_{1} = S I_{2} + 800 \Rightarrow \frac{35 P}{100} = \frac{27 P}{100} + 800 \Rightarrow \frac{35 P}{100} - \frac{27 P}{100} = 800 \Rightarrow \frac{8 P}{100} = 800 \Rightarrow P = \frac{800 \times 100}{8} \Rightarrow P = R s . 10000 S o, t h e o r i g i n a l s u m o f m o n e y = R s . 10000$

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