Question

In how many years will Rs.800 amounts to Rs.882 at 5% per annum compounded annually?

Answer 1

Step-by-step explanation:

SEE THE ABOVE ATTACHMENT

Answer 2

$\large\sf\underline{Given}$

• Principal = Rs. 800

• Amount = Rs. 882

• Rate = 5 % per annum

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$\large\sf\underline{To\:find}$

• Years / Time

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$\large\sf\underline{Solution}$

We know ,

$\small{\underline{\boxed{\mathrm\purple{A=P[1+\frac{r}{100}]^{n}}}}}$

Now substituting the value in the formula :

$\sf➞\:882=800[1+\frac{5}{100}]^{n}$

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$\sf➞\:\frac{882}{800}=[1+\frac{5}{100}]^{n}$

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$\sf➞\:\frac{441}{400}=[\frac{100+5}{100}]^{n}$

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$\sf➞\:\frac{441}{400}=[\frac{105}{100}]^{n}$

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$\sf➞\:\frac{441}{400}=[\frac{21}{20}]^{n}$

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$\sf➞\:[\frac{21}{20}]^{2}=[\frac{21}{20}]^{n}$

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⠀⠀⠀⠀⠀─━━━━━━━━━━━━─

• Using the law of indicies :

⠀⠀⠀⠀⠀$\sf➞\:a^{m}=a^{n}$

⠀⠀⠀⠀⠀$\sf➞\:m=n$

‎ ⠀⠀⠀⠀⠀─━━━━━━━━━━━━─

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${\sf{{\pink{➞\:2=n}}}}$

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$\small{\underline{\boxed{\mathrm\red{➠\:n=2\:yrs}}}}$

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!! Hope it helps !!