Question

In how many years will Rs 1600 amount to Rs 1936 at 10% annum when
compounded annually?
​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Principal, (P) = Rs.1600
• Amount, (A) = Rs.1936
• Rate, (R) = 10% p.a

$\underline{\bf{Explanation\::}}$

As we know that formula of the compounded annually;

$\boxed{\bf{Amount = Principal\bigg(1+\frac{R}{100} \bigg)^{n}}}$

A/q

$\longrightarrow\tt{A = P\bigg(1+\dfrac{R}{100} \bigg)^{n}}$

$\longrightarrow\tt{1936 = 1600 \bigg(1+\dfrac{10}{100} \bigg)^{n}}$

$\longrightarrow\tt{1936 = 1600 \bigg(1+ \cancel{\dfrac{10}{100}} \bigg)^{n}}$

$\longrightarrow\tt{1936 = 1600 \bigg(1+\dfrac{1}{10} \bigg)^{n}}$

$\longrightarrow\tt{1936 = 1600 \bigg(\dfrac{10+1}{10} \bigg)^{n}}$

$\longrightarrow\tt{1936 = 1600 \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\tt{\dfrac{1936}{1600} = \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\tt{\cancel{\dfrac{1936}{1600}} = \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\tt{\dfrac{121}{100} = \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\tt{\sqrt{\dfrac{121}{100} } = \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\tt{\bigg(\dfrac{11}{10}\bigg)^{2} = \bigg(\dfrac{11}{10} \bigg)^{n}}$

$\longrightarrow\bf{ n =2\:years}$

Thus,

The period of the Interest will be 2 years .

Answer 2

Answer:

above answer is correct

n= 2 year