Question

2. Calculate the amount and compound interest for 40000 at 6% p.a. compound interest for 3 years using the formula for simple interest.
​

Answer 1

AnswEr :

$\bf{Given}\begin{cases}\sf{Principal=Rs.\:40000}\\\sf{Time=3\:year}\\ \sf{Rate=6\% \: compounded\:annually}\end{cases}$

$\bf{Compound\:interest}\textsf{ is calculated on the} \\ \textsf{principal amount and also on the accumulated} \\\textsf{interest of previous periods, and can thus be} \\ \textsf{regarded as \bf{interest on interest.}}$

$\textsf{But, Here we won't use the Formula of} \\ \textsf{Compound Interest. we will use Simple}\\ \textsf{Interest Formula Only.}\\\\\bullet\:\:\textsf{Interest on First Year of Simple Interest}\\ \quad\textsf{and Compound Interest are always equal.}\\\\\bullet \:\: \textsf{Principal for Compound Interest for next}\\\quad\textsf{consecutive years can be find by Adding}\\ \quad\textsf{Principal and Past Year Interest.}$

$\rule{150}{2}$

$\underline{\bf\dag \:\large{\textit{Year 1 :}}}$

$\bf{we\:have}\begin{cases}\sf{Principal=Rs.\:40000}\\\sf{Time=1 \:year}\\ \sf{Rate=6\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:40000\times 6 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:240000}{100} \\\\\\:\implies \green{\sf Interest = Rs.\:2400}$

$\rule{200}{1}$

$\underline{\bf\dag \:\large{\textit{Year 2 :}}}$

$\bf{we\:have}\begin{cases}\sf{Principal=Rs. \:(40000 + 2400)}\\\qquad \qquad\sf{= Rs.\:42400}\\\sf{Time=1\:year}\\\sf{Rate=6\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:42400\times 6 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:254400}{100} \\\\\\:\implies \green{\sf Interest = Rs.\:2544}$

$\rule{200}{1}$

$\underline{\bf\dag \:\large{\textit{Year 3 :}}}$

$\bf{we\:have}\begin{cases}\sf{Principal=Rs. \:(42400 + 2544)}\\\qquad \qquad\sf{= Rs.\:44944}\\\sf{Time=1\:year}\\\sf{Rate=6\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:44944\times 6 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:269664}{100} \\\\\\:\implies \green{\sf Interest = Rs.\:2696.64}$

$\rule{200}{2}$

• C O M P O U N D ⠀I N T E R E S T :

↠ CI = (1st + 2nd + 3rd) Year Interest

↠ CI = Rs. (2400 + 2544 + 2696.64)

↠ CI = Rs. 7640.64

⠀

∴ CI after 3 years will be Rs. 7,640.64

$\rule{200}{2}$

• A M O U N T :

↠ Amount = Principal + CI

↠ Amount = Rs. (40,000 + 7,640.64)

↠ Amount = Rs. 47,640.64

⠀

∴ Amount after 3 years is Rs. 47,640.64

Answer 2

$\bf{\Huge{\boxed{\tt{\purple{ANSWER\::}}}}}$

$\bf{Given}\begin{cases}\sf{Principal,[P]\:=\:Rs.40000}\\ \sf{Rate,[R]\:=\:6\%}\\ \sf{Time,[T]\:=\:3\:years}\end{cases}}$

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The amount and compound Interest using by formula of S.I.

$\bf{\Large{\underline{\tt{\green{Explanation\::}}}}}$

Formula of the simple Interest, we get;

$\bf{\Large{\boxed{\sf{Simple\:Interest,[S.I.]\:=\:\frac{P*R*T}{100} }}}}}$

$\bf{\huge{\underline{\sf{\orange{\bigstar{1st\:Case\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal,[P]\:=\:Rs.40000}\\ \sf{Rate,[R]\:=\:6\%}\\ \sf{Time,[T]\:=\:1\:years}\end{cases}}$

$\implies\sf{S.I.\:=\:\frac{400\cancel{00}*6*1}{\cancel{100}} }$

$\implies\sf{S.I.\:=\:Rs.(400*6*1)}$

$\implies\sf{\red{S.I.\:=\:Rs.2400}}$

$\bf{\huge{\underline{\sf{\orange{\bigstar{2nd\:Case\;:}}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal,[P]\:=\:Rs.(40000+2400)}\\ \sf{Principal,[P]\:=\:Rs.42400}\\ \sf{Rate,[R]\:=\:6\%}\\ \sf{Time,[T]\:=\:1\:years}\end{cases}}$

$\implies\sf{S.I.\:=\:\frac{42400*6*1}{100} }$

$\implies\sf{S.I.\:=\:\frac{424\cancel{00}*6*1}{\cancel{100}} }$

$\implies\sf{S.I.\:=\:Rs.(424*6*1)}$

$\implies\sf{\red{S.I.\:=\:Rs.2544}}$

$\bf{\huge{\underline{\sf{\orange{\bigstar{3rd\:Case\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal,[P]\:=\:Rs.(42400+2544)}\\ \sf{Principal,[P]\:=\:Rs.44944}\\ \sf{Rate,[R]\:=\:6\%}\\ \sf{Time\:=\:1\:years}\end{cases}}$

$\implies\sf{S.I.\:=\:\frac{44944*6*1}{100} }$

$\implies\sf{S.I.\:=\:\cancel{Rs.\bigg(\frac{269664}{100}}\bigg) }$

$\implies\sf{\red{S.I.\:=\:Rs.2696.64}}$

___________________________________

Principal of the third year was Rs.44944 and so amount at the end of the third year = Rs.(44944 + 2696.64)

$\leadsto\sf{\bigstar\tt{Amount\:[A]\:=\:Rs.47640.64}}}$

Therefore,

We know that, compound Interest:

$\implies\sf{C.I.\:=\:Amount\:-\:Principal}$

$\implies\sf{C.I.\:=\:Rs.47640.64\:-\:Rs.40000}$

$\implies\sf{\red\boxed{\tt{C.I.\:=\:Rs.7640.64}}}$

Thus,

$\sf{\Large{\boxed{\bigstar{\tt{Amount\:=\:Rs.47640.64}}}}}$

$\sf{\Large{\boxed{\bigstar{\tt{C.I.\:=\:Rs.7640.64}}}}}$