Question

At what rate percent per annum will Rs 5000 amount to Rs 5832 in 2 years, compounded annually?

1 point

(a) 11℅

(b) 10℅

(c) 9℅

(d) 8℅

give the answer in percent
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Answer 1

S O L U T I O N :

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

• Principal, (P) = Rs.5000
• Amount, (A) = Rs.5832
• Time, (n) = 2 years

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

As we know that formula of the compounded annually;

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

A/q

$\mapsto\tt{5832 = 5000\bigg(1+\dfrac{R}{100} \bigg)^{2}}$

$\mapsto\tt{\dfrac{5832}{5000}= \bigg(1+\dfrac{R}{100} \bigg)^{2}}$

$\mapsto\tt{\cancel{\dfrac{5832}{5000}}= \bigg(1+\dfrac{R}{100} \bigg)^{2}}$

$\mapsto\tt{\dfrac{2916}{2500}= \bigg(1+\dfrac{R}{100} \bigg)^{2}}$

$\mapsto\tt{\sqrt{\dfrac{2916}{2500} } = \bigg(1+\dfrac{R}{100} \bigg)}$

$\mapsto\tt{\dfrac{54}{50} = \bigg(1+\dfrac{R}{100} \bigg)}$

$\mapsto\tt{\dfrac{54}{50} - 1 = \dfrac{R}{100}}$

$\mapsto\tt{\dfrac{54-50}{50} = \dfrac{R}{100}}$

$\mapsto\tt{\dfrac{4}{50} = \dfrac{R}{100}}$

$\mapsto\tt{50R = 400\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{R=\cancel{ 400/50}}$

$\mapsto\bf{R=8\:\%}$

Thus,

The rate percent of compounded annually per annum will be 8% .

Answer 2

Step-by-step explanation:

hope it will help