JIPMAT 2024 (QA) - An amount doubles itself at compound interest in 5 years. How many years will it take to make the amount 16 times itself ? | PYQs + Solutions

JIPMAT 2024

Arithmetic

Simple & Compound Interest

Medium

An amount doubles itself at compound interest in 5 years. How many years will it take to make the amount 16 times itself ?

✅ Correct Option: 4

Let the initial amount be

P

and rate of interest be

r\%

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Given that amount doubles in 5 years:

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P(1 + \frac{r}{100})^5 = 2P

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(1 + \frac{r}{100})^5 = 2

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\newline

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Now, let's say it takes

x

years to make the amount 16 times:

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P(1 + \frac{r}{100})^x = 16P

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(1 + \frac{r}{100})^x = 16

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\newline

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We know that

16 = 2^4

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[(1 + \frac{r}{100})^5]^{\frac{x}{5}} = 2^4

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2^{\frac{x}{5}} = 2^4

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\newline

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Therefore:

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\frac{x}{5} = 4

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x = 20