Question

Find the compound interest when it is compounded
annually:
(1) P=625, R = 4% p.a., T = 2 years.
(ii) P=8000, R = 5% p.a., T = 3 years.
(iii) P=3200, R = 25% p.a., T = 3 years.​

Answer 1

Solution :

Firstly, we know that formula of the compounded annually;

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

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

(1) : Principal, (P) = 625 , Rate, (R) = 4% p.a & Time, (n) = 2 Years

$\mapsto\sf{A=625 \bigg(1+\cancel{\dfrac{4}{100}} \bigg)^{2}}\\\\\\\mapsto\sf{A=625 \bigg(1+\dfrac{1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625\bigg(\dfrac{25+1}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=625\bigg(\dfrac{26}{25} \bigg)^{2}}\\\\\\\mapsto\sf{A=\cancel{625} \times \dfrac{26}{\cancel{25}} \times \dfrac{26}{\cancel{25}}} \\\\\\\mapsto\sf{A=Rs.(1\times 26\times 26)}\\\\\mapsto\bf{A=Rs.676}$

Now;

As we know that compound Interest;n

$\longrightarrow\sf{C.I. = Amount-Principal}\\\\\longrightarrow\sf{C.I. = Rs.676 - Rs.625}\\\\\longrightarrow\bf{C.I. = Rs.51}$

(2) : Principal, (P) = 8000 , Rate, (R) = 5% p.a & Time, (n) = 3 Years

$\mapsto\sf{A=8000\bigg(1+\cancel{\dfrac{5}{100}} \bigg)^{3}}\\\\\\\mapsto\sf{A=8000\bigg(1+\dfrac{1}{20} \bigg)^{3}}\\\\\\\mapsto\sf{A=8000\bigg(\dfrac{20+1}{20} \bigg)^{3}}\\\\\\\mapsto\sf{A=8000\bigg(\dfrac{21}{20} \bigg)^{3}}\\\\\\\mapsto\sf{A=\cancel{8000} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} \times \dfrac{21}{\cancel{20}} }\\\\\\\mapsto\sf{A=Rs.(1\times 21\times 21\times 21)}\\\\\mapsto\bf{A=Rs.9261}$

Now;

$\longrightarrow\sf{C.I. = Amount-Principal}\\\\\longrightarrow\sf{C.I. = Rs.9261- Rs.8000}\\\\\longrightarrow\bf{C.I. = Rs.1261}$

(3) : Principal, (P) = 3200 , Rate, (R) = 25% p.a & Time, (n) = 3 Years

$\mapsto\sf{A=3200\bigg(1+\cancel{\dfrac{25}{100}} \bigg)^{3}}\\\\\\\mapsto\sf{A=3200\bigg(1+\dfrac{1}{4} \bigg)^{3}}\\\\\\\mapsto\sf{A=3200\bigg(\dfrac{4+1}{4} \bigg)^{3}}\\\\\\\mapsto\sf{A=3200\bigg(\dfrac{5}{4} \bigg)^{3}}\\\\\\\mapsto\sf{A=\cancel{3200} \times \dfrac{5}{\cancel{4}} \times \dfrac{5}{\cancel{4}} \times \dfrac{5}{\cancel{4}} }\\\\\\\mapsto\sf{A=Rs.(50\times 5\times 5\times 5)}\\\\\mapsto\bf{A=Rs.6250}$

Now;

$\longrightarrow\sf{C.I. = Amount-Principal}\\\\\longrightarrow\sf{C.I. = Rs.6250 - Rs.3200}\\\\\longrightarrow\bf{C.I. = Rs.3050}$

Answer 2

Step-by-step explanation:

I hope that it's helpful for you