Question

find the amount and the compound interest on$16000 for 3years at 5%per annum compounded annually​

Answer 1

S O L U T I O N :

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

• Principal, (P) = Rs.16000
• Rate, (R) = 5% p.a
• 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

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

$\mapsto\tt{A =16000 \bigg(1+\dfrac{5}{100} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(1+\cancel{\dfrac{5}{100} }\bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(1+\dfrac{1}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(\dfrac{20+1}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000 \bigg(\dfrac{21}{20} \bigg)^{3}}$

$\mapsto\tt{A =16000\times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} }$

$\mapsto\tt{A =\cancel{16000} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} }$

$\mapsto\tt{A = Rs.(2 \times 21 \times 21 \times 21)}$

$\mapsto\bf{A = Rs.18522}$

Now, as we know that compound Interest;

→ C.I. = Amount - Principal

→ C.I. = Rs.18522 - Rs.16000

→ C.I. = Rs.2522

Thus,

The amount & compound Interest will be Rs.18522 & Rs.2522 .