Question

.
Calculate compound interest on 1000 over a period of 1 year at 10% per annum, if interest is compounded quarterly?​

Answer 1

Answer:

9000 is the 90;% annum is the answer

Answer 2

Solution :

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

• Principal, (P) = Rs.1000
• Time, (n) = 1 year
• Rate, (R) = 10% p.a.

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

Using formula of the compounded quarterly :

$\boxed{\bf{Amount =Principal\bigg(1+\frac{R}{4\times 100} \bigg)^{4n}}}}$

A/q

$\longrightarrow\sf{A=1000\bigg(1+\dfrac{\cancel{10}}{4\times 10\cancel{0}} \bigg)^{(4\times 1)}}\\\\\\\longrightarrow\sf{A= 1000\bigg(1+\dfrac{1}{40} \bigg)^{4}}\\\\\\\longrightarrow\sf{A= 1000\bigg(\dfrac{40 + 1}{40} \bigg)^{4}}\\\\\\\longrightarrow\sf{A=1000\bigg(\dfrac{41}{40} \bigg)^{4}}\\\\\\\longrightarrow\sf{A=1000\times \dfrac{41}{40} \times \dfrac{41}{40} \times \dfrac{41}{40} \times \dfrac{41}{40} }$

$\longrightarrow\sf{A=\dfrac{1\cancel{000} \times 41\times 41\times 41\times 41}{2560\cancel{000}} }\\\\\\\longrightarrow\sf{A= \dfrac{41\times 41\times 41 \times 41}{2560} }\\\\\\\longrightarrow\sf{A= \cancel{\dfrac{2825761}{2560} }}\\\\\\\longrightarrow\bf{A=Rs.1103.81}$

Now;

As we know that compound Interest;

$\mapsto\sf{C.I.= Amount - Principal}\\\\\mapsto\sf{C.I. = Rs.1103.81 - Rs.1000}\\\\\mapsto\bf{C.I. = Rs.103.81}$

Thus;

The compound Interest will be Rs.103.81 .