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Question

At compound interest rate if a certain sum of money doubles in n years then the amount will be four-fold in ______.


A

2n2 years

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B

n2 years

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C

2n years

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D

4n years

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Solution

The correct option is C

2n years



Let principal = ₹x and rate = R
According to question,
x(1+R100)n=2x -------(i)
(1+R100)n=2-------(ii)
Let it become 4 folds in N years.

x(1+R100)N=4x

x(1+R100)N=2×2x

Substitutuing the value of 2 and 2x from (i) and (ii) we get

x(1+R100)N=[(1+R100)n][x(1+R100)n]

(1+R100)N=(1+R100)n(1+R100)n


N=2n years


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