Question

A man imvested rs 12000 at 5% p.a. c.i. for three years. Calculate i)the amount at the end of second year ii)interest earned in the third year iii)amount at the end of third year​

Answer 1

AnswEr :

$\bf{ Given}\begin{cases}\textsf{Principal = Rs. 12000}\\\sf{Rate = 5\% \:compounded \:annually}\\ \textsf{Time = 3 years}\end{cases}$

i ) The amount at the end of second year :

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

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

$\rule{100}{2}$

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

$\bf{we\:have}\begin{cases}\sf{Principal=Rs.\:12000}\\\sf{Time=1 \:year}\\ \sf{Rate=5\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:12000 \times 5 \times 1}{100} \\ \\ \\:\implies \sf Interest =\cancel\dfrac{Rs.\:60000}{100} \\ \\ \\:\implies \green{\sf Interest = Rs.\:600}$

$\rule{200}{1}$

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

$\bf{we\:have}\begin{cases}\sf{Principal=Rs. \:(12000 + 600)}\\\qquad \qquad\sf{= Rs.\:12600}\\\sf{Time=1\:year}\\\sf{Rate=5\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:12600\times 5 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:63000}{100} \\\\\\:\implies \green{\sf Interest = Rs.\:630}$

$\rule{200}{1}$

• AMOUNT⠀AFTER⠀2ND⠀YEAR :

↠ Amount = Principal + 1st year + 2nd year

↠ Amount = Rs.(12000 + 600 + 630)

↠ Amount = Rs. 13230

⠀

∴ Amount after 2 years is Rs.13230.

$\rule{300}{2}$

ii ) Interest earned in the third year :

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

$\bf{we\:have}\begin{cases}\sf{Principal=Rs. \:(12600 + 630)}\\\qquad \qquad\sf{= Rs.\:13230}\\\sf{Time=1\:year}\\\sf{Rate=5\% \:p.a.}\end{cases}$

$:\implies \sf Interest = \dfrac{Principal \times Rate\times Time}{100} \\ \\\\:\implies \sf Interest = \dfrac{Rs. \:13230\times 5 \times 1}{100} \\ \\ \\:\implies \sf Interest = \cancel\dfrac{Rs.\:66150}{100}\\\\\\:\implies \blue{\sf Interest = Rs.\:661.50}$

⠀

∴ Interest earned in 3rd yr is Rs. 661.50.

$\rule{300}{2}$

iii ) Amount at the end of third year :

↠ Amount = 2yr Amount + 3rd yr Interest

↠ Amount = Rs.(13230 + 661.50)

↠ Amount = Rs. 13891.50

⠀

∴ Amount after 3 years is Rs. 13891.50.

Answer 2

$\bf{\Huge{\boxed{\sf{\blue{ANSWER\::}}}}}}$

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

A man invested Rs.12000 at 5% per annum compound Interest for three years.

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

Calculate as;

• The amount at the end of second year.
• Interest earned in the third year.
• Amount at the end of third year.

$\bf{\Large{\underline{\sf{\red{Explanation\::}}}}}$

$\bf{\Large{\boxed{\tt{\orange{First\:Case\::}}}}}}$

We have 3 years total time given, according to question we suppose 2 years, we get;

$\bf{We\:have}\begin{cases}\sf{Principal,[P]\:=\:Rs.12000}\\ \sf{Time,[T]\:=\:1\:years}\\ \sf{Rate,[R]\:=\:5\%}\end{cases}}$

We know that formula of the C.I. = Amount - Principal.

Or

$\leadsto\sf{\orange{A=P(1+\frac{R}{100} )^{n} }}$

Therefore,

$\longmapsto\rm{A=12000*(1+\frac{5}{100} )^{2} }$

$\longmapsto\rm{A=12000*(1+\frac{\cancel{5}}{\cancel{100}} )^{2} }$

$\longmapsto\sf{A=12000*(1+\frac{1}{20} )^{2} }$

$\longmapsto\rm{A=12000*(\frac{20+1}{20} )^{2} }$

$\longmapsto\rm{A=12000*\frac{21}{20} *\frac{21}{20} }$

$\longmapsto\rm{A=\cancel{12000}*\frac{21}{\cancel{20}} *\frac{21}{\cancel{20}} }$

$\longmapsto\rm{A\:=\:Rs.(30*21*21)}$

$\longmapsto\rm{\pink{A\:=\:Rs.13230}}$

$\bf{\Large{\boxed{\tt{\orange{Second\:Case\::}}}}}}$

We know that formula of the Simple Interest;

$\leadsto\sf{\orange{S.I.\:=\:\frac{P*R*T}{100} }}$

• Principal,[P] = Rs.12000
• Rate,[R] = 5%
• Time,[T] = 3 years.

Therefore,

$\longmapsto\tt{S.I.\:=\:\frac{12000*5*3}{100} }$

$\longmapsto\tt{S.I.\:=\:\frac{120\cancel{00}*5*3}{\cancel{100}} }$

$\longmapsto\tt{S.I.\:=\:Rs.(120*15)}$

$\longmapsto\tt{\pink{S.I.\:=\:Rs.1800}}$

$\bf{\Large{\boxed{\tt{\orange{Third\:Case\::}}}}}}$

$\bf{We\:have}\begin{cases}\tt{Principal,[P]\:=\:Rs.12000}\\ \tt{Rate,[R]\:=\:5\%}\\ \tt{Time,[n]\:=\:3\:years}\end{cases}}$

Therefore,

$\longmapsto\sf{A\:=\:P(1+\frac{R}{100} )^{n} }$

$\longmapsto\sf{A\:=\:12000*(1+\frac{5}{100} )^{3} }$

$\longmapsto\sf{A\:=\:12000*(1+\frac{\cancel{5}}{\cancel{100}} )^{3} }$

$\longmapsto\sf{A\:=\:12000*(1+\frac{1}{20} )^{3} }$

$\longmapsto\sf{A\:=\:12000*(\frac{20+1}{20})^{3} }$

$\longmapsto\sf{A\:=\:12000*\frac{21}{20} *\frac{21}{20} *\frac{21}{20} }$

$\longmapsto\sf{A\:=\:\cancel{12000}*\frac{21}{\cancel{20}} *\frac{21}{\cancel{20}} *\frac{21}{2\cancel{0}} }$

$\longmapsto\sf{A\:=\:\frac{3*21*21*21}{2} }$

$\longmapsto\sf{A\:=\:Rs.(\cancel{\frac{27783}{2} })}$

$\longmapsto\sf{\pink{A\:=\:Rs.13891.5}}$

Thus,

The amount at the end of third year is Rs.13891.5.