Question

In what time will ₹ 1600 amount to ₹ 2025 and 12 % per annum compounded annually

Answer 1

Question Correction :In what time will ₹ 1600 amount to ₹ 2025 and 12.5 % per annum compounded annually .

$\mathfrak{Answer:}$

= 2 years.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\bold{Given\:in\:the\:Question:}}$

• Principle = P = Rs. 1600.
• Amount = A = Rs. 2025.
• Rate = r = 12.5%.
• Interest is compounded annually.

$\bold{Solution:}$

Let the time be n years.

We know that ,

$\boxed{\bold{Amount=P\left(1+\dfrac{r}{100}\right)^n}}\\\\\\\mathfrak{According\:to\:question:}\\\\\\\implies\tt{2025=1600\left(1+\dfrac{12.5}{100}\right)^n}\\\\\\\implies\tt{\dfrac{2025}{1600}=\left(\dfrac{9}{8}\right)^n}\\\\\\\implies\tt{\dfrac{81}{64}=\left(\dfrac{9}{8}\right)^n}\\\\\\\implies\tt{\left(\dfrac{9}{8}\right)^2=\left(\dfrac{9}{8}\right)^n}\\\\\\\implies\tt{n=2.}\\\\\\\\\boxed{\boxed{\bold{Time=2\:years.}}}$

Answer 2

$\underline{\bold{Given:}}$

Principle = Rs.1600

Amount = Rs.2025

Rate = 12.5% per annum.

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

Time = ??

Compounded annually,

We know that,

$\boxed{\bold{Amount = P{(1 +\dfrac{r}{100})}^{n}}}$

$\bold{let\:the\:time\:be\:n\:years.}$

$\implies\bold{2025 = 1600 {( 1 + \dfrac{12.5}{100})}^{n}}$

$\implies\bold{2025 =1600{(\dfrac{9}{8})}^{n}}$

$\implies\bold{\dfrac{2025}{1600} = {(\dfrac{9}{8})}^{n}}$

$\implies\bold{\dfrac{81}{64} = {(\dfrac{9}{8})}^{n}}$

$\implies\bold{{(\dfrac{9}{8})}^{2} = {(\dfrac{9}{8})}^{n}}$

We know that , when the fractions are equal then the powers are also equal....

$\implies\bold{2 = n}$

$\therefore{\bold{Time = 2years}}$