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Mathematics

What sum will amount to ₹ 6,593.40 in 2 years at C.I., if the rates are 10 percent and 11 percent for the two successive years ?

Compound Interest

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Answer

Let sum be ₹ x.

For first year :

P = ₹ x

R = 10%

T = 1 year

I = P×R×T100=x×10×1100=x10\dfrac{P \times R \times T}{100} = \dfrac{x \times 10 \times 1}{100} = \dfrac{x}{10}

Amount = P + I = x+x10=11x10x + \dfrac{x}{10} = \dfrac{11x}{10}.

For second year :

P = ₹ 11x10\dfrac{11x}{10}

R = 11%

T = 1 year

I = P×R×T100=11x10×11×1100=121x1000\dfrac{P \times R \times T}{100} = \dfrac{\dfrac{11x}{10} \times 11 \times 1}{100} = \dfrac{121x}{1000}

Amount = P + I = 11x10+121x1000=1100x+121x1000=1221x1000\dfrac{11x}{10} + \dfrac{121x}{1000} = \dfrac{1100x + 121x}{1000} = \dfrac{1221x}{1000}.

Given,

Amount after two years = ₹ 6593.40

1221x1000=6593.40x=6593.40×10001221x=5.4×1000=5400.\therefore \dfrac{1221x}{1000} = 6593.40 \\[1em] \Rightarrow x = \dfrac{6593.40 \times 1000}{1221} \\[1em] \Rightarrow x = 5.4 \times 1000 = 5400.

Hence, required sum = ₹ 5400.

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