A certain sum of money invested at compound i | vedclass

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(D) Let the principal (sum of money) be $P = 100$.Given that the amount after $2$ years at compound interest is $1.44$ times the principal, so $A = 14

Vedclass · Accepted Answer

$5$

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(D) Let the principal (sum of money) be $P = 100$.Given that the amount after $2$ years at compound interest is $1.44$ times the principal, so $A = 144$.Using the compound interest formula: $A = P(1 + \frac{R}{100})^n$$144 = 100(1 + \frac{R}{100})^2$$(1 + \frac{R}{100})^2 = \frac{144}{100} = 1.44$$1 + \frac{R}{100} = \sqrt{1.44} = 1.2$$\frac{R}{100} = 0.2 \Rightarrow R = 20\%$.Now, we consider twice the original sum, so the new principal $P' = 2 	imes 100 = 200$.We want this sum to double itself, so the new amount $A' = 2 	imes 200 = 400$.The simple interest required is $SI = A' - P' = 400 - 200 = 200$.Using the simple interest formula: $SI = \frac{P' 	imes R 	imes T}{100}$$200 = \frac{200 	imes 20 	imes T}{100}$$200 = 40 	imes T$$T = \frac{200}{40} = 5$ years.

$A$ certain sum of money invested at compound interest becomes $1.44$ times of itself in $2$ years. If twice this sum were lent at simple interest, in how many years would it double itself?

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