Question

In how many e years 1000 rupees amount to do 1464 point 10 if the rate of the interest is 10% P.A compounded annually

Answer 1

$\sf{\bold{\green{\underline{\underline{Correct\: Question}}}}}$

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• In how many years 1000 rupees amount to Rs. 1464.10 if the rate of the interest is 10% P.A compounded annually

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$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Amount = Rs. 1464.10
• Principle = Rs. 1000
• Rate = 10%

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Time = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{Amount = Principle \bigg\lgroup 1 + \dfrac{rate}{10}\bigg\rgroup^{time}}}}}$

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$\sf :\implies\: {\bold{ 1464.1 = 1000 \bigg\lgroup 1 + \dfrac{10}{100} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ 1464.1 = 1000 \bigg\lgroup 1 + \dfrac{1}{10} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ 1464.1 = 1000 \bigg\lgroup \dfrac{10 + 1 }{10} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ 1464.1 = 1000 \bigg\lgroup \dfrac{11}{10} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ \dfrac{1464.1}{1000}= \bigg\lgroup \dfrac{11}{10} \bigg\rgroup^{time} }}$

$\sf :\implies\: {\bold{ \dfrac{14641}{10000}= \bigg\lgroup \dfrac{11}{10} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ \dfrac{11\times 11\times 11 \times 11}{10\times 10\times 10 \times 10}= \bigg\lgroup \dfrac{11}{10} \bigg\rgroup^{time} }}$

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$\sf :\implies\: {\bold{ \bigg\lgroup \dfrac{11}{10}\bigg\rgroup ^4= \bigg\lgroup \dfrac{11}{10} \bigg\rgroup^{time} }}$

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• Acc. to the law of exponent same bases implies same power

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$\sf :\implies\: {\bold{time = 4 years }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• In 4 years Rs. 1000 will amount to Rs.1464.10 at 10% per annum

Answer 2

Answer:

✯ Given :-

• Principal (P) = Rs 1000
• Amount (A) = Rs 1464.10
• Rate of Interest (r%) = 10 %

✯ To Find :-

• How many years Rs 1000 amount will be Rs 1464.10 at 10 % per annum.

✯ Formula Used :-

$\boxed{\bold{\large{✮\: P(1\: +\: \dfrac{r}{100})^{n}} = A}}$

✯ Solution :-

⋆ Given :

• P = Rs 1000
• A = Rs 1464.10
• r% = 10 %

➣ According to the question by using the formula we get,

➨ 1000 ( 1 + $\sf\dfrac{\cancel{10}}{\cancel{100}}$ )ⁿ = 1464.10

➨ ( 1 + $\dfrac{1}{10}$ )ⁿ = $\dfrac{146410}{1000 × 100}$

➨ ( 1 + $\dfrac{1}{10}$ )ⁿ = $\dfrac{14641}{10000}$

➨ ( $\dfrac{11}{10}$ )ⁿ = ( $\dfrac{11}{10}$ )⁴

➠ n = 4 years

$\therefore$ In 4 years Rs 1000 amount will be Rs 1464.10 at the 10 % per annum.

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