Question

find compound interest and amount for Rs 8000
at the rate of 5% for 3 years.
interest payable
yearly.​

Answer 1

Given :

Principle : ₹8000

Rate of interest : 5%

Time : 3 years

To find :

The compound interest and the amount if it's compound anually.

Solution :

First, we'll find the amount by it's formula.

$\sf \dashrightarrow Amount = Principle \bigg( 1 + \dfrac{Rate}{100} \bigg)^{Time}$

$\sf \dashrightarrow 8000 \bigg( 1 + \dfrac{5}{100} \bigg)^{3}$

$\sf \dashrightarrow 8000 \bigg( 1 + \dfrac{1}{20} \bigg)^{3}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{20 + 1}{20} \bigg)^{3}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{21}{20} \bigg)^{3}$

$\sf \dashrightarrow 8000 \bigg( \dfrac{21^3}{20^3} \bigg)$

$\sf \dashrightarrow 8000 \bigg( \dfrac{9261}{8000} \bigg)$

$\sf \dashrightarrow \dfrac{8000 \times 9261}{8000} = \dfrac{74088000}{8000}$

$\sf \dashrightarrow \cancel \dfrac{7408800}{8000} = 9261$

Now, we can find the compound interest.

Compound interest :

$\sf \dashrightarrow Amount - Principle$

$\sf \dashrightarrow 9261 - 8000$

$\dashrightarrow$₹$\sf 1261$

Hence, the amount and compound interest are ₹9261 and ₹1261 respectively.

Answer 2

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

$\qquad\sf{:\implies\:Principle\:=\:Rs.\:8000}$

$\qquad\sf{:\implies\:Rate\:=\:5\:\%}$

$\qquad\sf{:\implies\:Time\:=\:3\:years}$

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

$\qquad\sf{:\implies\:Compound \:interest\: }$

$\qquad\sf{:\implies\:Amount}$

$\underline{\underline{\sf{\maltese\:Concept\::-}}}$

$\odot$ Here we have given that the principal is Rs. 8000, rate is 5% and time is 3 years so firstly we will find out the amount by substituting the given values in the formula

• $\boxed{\sf{Amount\:=\:Principle\: \left\{\:1\:+\dfrac{Rate}{100} \:\right\}^{Time}}}$

$\odot$ After finding the amount we will find out the compound interest by substituting the values in the formula

• $\boxed{\sf{Compound\:interest\:=\:Amount\:-\:Principle}}$

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

$\underline{\underline{\sf{\maltese\:Full\:Solution\::-}}}$

~Let us find out the amount by substituting the give values in the formula

$\boxed{\sf{Amount\:=\:Principle\: \left\{\:1\:+\dfrac{Rate}{100} \:\right\}^{Time}}}$

$\qquad\sf{:\implies\:Amount\:=\:Principle\: \left\{\:1\:+\dfrac{Rate}{100} \:\right\}^{Time}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\: \left\{\:1\:+\dfrac{5}{100} \:\right\}^{3}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\: \left\{\:1\:+\dfrac{1}{20} \:\right\}^{3}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\: \left\{ \:\dfrac{20\:+\:1}{20} \:\right\}^{3}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\: \left\{ \:\dfrac{21}{20} \:\right\}^{3}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\: \left\{ \:\dfrac{\:9261\:}{\:8000\:} \:\right\}}$

$\qquad\sf{:\implies\:Amount\:=\:8000\:\times \:\dfrac{\:9261\:}{\:8000\:}}$

$\qquad\sf{:\implies\:Amount\:=\:9261}$

$\therefore$

$\underline{\sf{Hence\:the\:amount\:is\;9261\:.}}$

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$

~Let us find out the compound interest by using the formula

$\boxed{\sf{Compound\:interest\:=\:Amount\:-\:Principle}}$

$\qquad\sf{:\implies\:Compound\:interest\:=\:Amount\:-\:Principle}$

$\qquad\sf{:\implies\:Compound\:interest\:=\:9261\:-\:8000}$

$\qquad\sf{:\implies\:Compound\:interest\:=\:Rs.\:1261}$

$\therefore$

$\underline{\sf{Hence\:the\:compound\:interest\:is\:Rs.\:1261}}$

$\qquad\qquad\underline{\qquad\qquad\qquad\qquad\qquad\qquad}$