Question

In how many years will Rs 4000 amount to Rs 4630.50 at 5% per annum compounded annually ?
Ans - 3 Years but how ???​

Answer 1

AnswEr :

• Amount = Rs. 4630.50
• Principal = Rs. 4000
• Rate = 5% p.a.
• Time = ?

• Formula for Amount of CI is :

$\longrightarrow \sf{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t}}$

$\longrightarrow \sf{4630.50 = 4000 \times \bigg(1 + \dfrac{5}{100} \bigg)^{t}}$

$\longrightarrow \sf{\cancel\dfrac{46305}{10} = 4000 \times \bigg(1 + \cancel\dfrac{5}{100} \bigg)^{t}}$

$\longrightarrow \sf{\dfrac{9261}{2} = 4000 \times \bigg(1 + \dfrac{1}{20} \bigg)^{t}}$

$\longrightarrow \sf{\dfrac{9261}{2 \times 4000} = \bigg(\dfrac{20 + 1}{20} \bigg)^{t}}$

$\longrightarrow \sf{\dfrac{9261}{8000} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\longrightarrow \sf{\bigg(\dfrac{21}{20} \bigg)^{3} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\longrightarrow \boxed{\sf t = 3 \: yrs.}$

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∴ the Time Period is for 3 Years.

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

→Amount = Rs. 4630.50

→Principal = Rs. 4000

→Rate = 5% p.a.

→Time = ?

So, simply by using the fromula of Amount of CI we can find the answer

$\implies \tt{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t}}$

$\implies \tt{4630.50 = 4000 \times \bigg(1 + \dfrac{5}{100} \bigg)^{t}}$

$\implies\tt{\cancel\dfrac{46305}{10} = 4000 \times \bigg(1 + \cancel\dfrac{5}{100} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{2} = 4000 \times \bigg(1 + \dfrac{1}{20} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{2 \times 4000} = \bigg(\dfrac{20 + 1}{20} \bigg)^{t}}$

$\implies \tt{\dfrac{9261}{8000} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\implies \tt{\bigg(\dfrac{21}{20} \bigg)^{3} = \bigg(\dfrac{21}{20} \bigg)^{t}}$

$\longrightarrow \boxed{\sf time = 3 \: yrs.}$

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