Question

At what rate per cent per annum will₹3000amount to ₹3993in 3years, interest being compounded annually?

Answer 1

S O L U T I O N :

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

• Principal,(P) = Rs.3000
• Amount, (A) = Rs.3993
• Time, (n) = 3 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

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

$\mapsto\tt{3993 = 3000\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{3993}{3000} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\cancel{\dfrac{3993}{3000}} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{\dfrac{1331}{1000} =\bigg(1+\dfrac{R}{100} \bigg)^{3}}$

$\mapsto\tt{3\sqrt{\dfrac{1331}{1000} } =1+\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{11}{10} =1+\dfrac{R}{100} }$

$\mapsto\tt{\dfrac{11}{10} -1 = \dfrac{R}{100} }$

$\mapsto\tt{\dfrac{11-10}{10} = \dfrac{R}{100} }$

$\mapsto\tt{\dfrac{1}{10} = \dfrac{R}{100} }$

$\mapsto\tt{10R = 100\:\:\underbrace{\sf{cross-multiplication}}}$

$\mapsto\tt{R = \cancel{100/10}}$

$\mapsto\bf{R = 10\:\%}$

Thus,

The rate percent per annum will be 10% .