Question

Question no.40!!!

Compound Interest question:

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Calculate the time in which any amount doubles itself at rate of 10% per annum compounded annually.
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Class-9(CICSE Board)
Subject-Mathematics

If you know how to calculate it,then go for it otherwise be away from this.


Hoping best answers.

Answer 1

Let the principal be 'x'.

Then the amount = 2P.

We know that A = P(1 + r/100)^n

⇒ 2P = P(1 + 10/100)^n

⇒ 2 = (1 + 1/10)^n

⇒ 2 = (11/10)^n

Apply log on both sides, we get

⇒ log 2 = log(11/10)^n

⇒ log 2 = n log(11/10)

⇒ log2/log(11/10) = n

⇒ n = ~7.2.

Therefore, the time = 7.2 years.

Hope it helps!

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

$<b>$Let principal be p.

So, the amount will be 2p.

As we know that:
$a = p(1 + \frac{r}{100}) {}^{n} \\ 2p = p(1 + \frac{10}{100} ) {}^{n} \\ 2 = (1 + \frac{1}{10} ) {}^{n} \\ 2 = ( \frac{11}{10} ) {}^{n}$
Now, we apply log to both the sides

So, we get

$log(2) = log( \frac{11}{10} ) {}^{n} \\ \\ log(2) = n \: log( \frac{11}{10} ) \\ \\ \frac{ log(2) }{ log( \frac{11}{10} ) } = n$

n = ~7.2

Therefore, Time = 7.2 years

$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\:helps\: you}}}}}}}}}}}}}}}$