Question

Find the amount and compound interest on ₹2500 for 2 years compounded annually, the rate of interest being 6% during the first year and 8% during the second year.

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Answer 1

Given :-

• ₹2500 for 2 years compounded annually, the rate of interest being 6% during the first year and 8% during the second year.

To Find :-

• Find the amount and compound interest  

Solution :-

~Here, we’re given the principal amount ( P ) , time and rate of interest ( R ) for the successive years. We need to find the compound interest ( CI ) and the amount ( A )

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Formula for this question :-

$\boxed{\sf{ \maltese \;\; A = P \bigg\{ 1 + \dfrac{ r }{100} \bigg\} \bigg\{ 1 + \dfrac{R}{100} \bigg\} }}$

Where,  

• A is amount which we need to find  
• P is the principal amount ( Rs. 2500 )  
• r is the rate of interest for first year ( 6 % )  
• R is the rate of interest for second year ( 8 % )  

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Finding the amount :-

$\sf \implies A = 2500 \bigg\{ 1 + \dfrac{6}{100} \bigg\} \bigg\{ 1 + \dfrac{8}{100} \bigg\}$  

$\sf \implies A = 2500 \bigg\{ \dfrac{106}{100} \bigg\} \bigg\{ \dfrac{108}{100} \bigg\}$

$\sf \implies A = 106 \times 27$  

$\boxed{\bf{ \bigstar \;\; Amount = Rs.\;2862 }}$

Finding the compound interest :-  

$\sf \implies Rs.\;2862 -Rs.\;2500$

$\boxed{\bf{ \bigstar \;\; CI = Rs. \;362 }}$

[ Note : We've not taken time in calculation because we have solved the interest for each year and any number raised to the power 1 is always the same number ]  

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Hence,  

• The amount is Rs. 2862 and Compound interest is Rs. 362  

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Answer 2

Given : ₹2500 for 2 years compounded annually, the rate of interest being 6% during the first year and 8% during the second year.

Exigency to find : The Amount and Compound interest .

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⠀⠀⠀⠀⠀Finding Amount :

$\dag\:\:\bf{ \gray{Formula,\:For\:this\:Question \::}}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Amount \:: P \bigg[ \bigg( 1 + \dfrac{r}{100}\bigg)^t\bigg]\bigg[\bigg( 1 + \dfrac{R}{100}\bigg) ^T\bigg] }\bigg\rgroup$

⠀⠀⠀⠀⠀Here P is the Principal (i.e 2,500 ) , r is the Rate of Interest for first year ( i.e 6 % ) , R is the Rate of Interest for second year ( i.e. 8% ) and T or t is the time if the interest devided in two parts so time will be also devided so t or time when interest is 6% is 1 & T or Time when interest is 8% is 1 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf Amount = 25,00 \bigg[ \bigg( 1 + \dfrac{6}{100}\bigg)^1\bigg]\bigg[ \bigg( 1 + \dfrac{8}{100}\bigg) ^1\bigg]$

$\qquad \longmapsto \sf Amount = 25,00 \bigg[ \bigg( 1 + \cancel {\dfrac{6}{100}}\bigg)^1\bigg]\bigg[ \bigg( 1 + \cancel {\dfrac{8}{100}}\bigg) ^1\bigg]$

$\qquad \longmapsto \sf Amount = 25,00 \bigg[ \bigg( 1 + 0.06 \bigg)^1\bigg]\bigg[ \bigg( 1 + 0.08 \bigg) ^1\bigg]$

$\qquad \longmapsto \sf Amount = 25,00 \bigg[ \bigg( 1.06 \bigg)^1\bigg]\bigg[ \bigg( 1.08 \bigg) ^1\bigg]$

$\qquad \longmapsto \sf Amount = 25,00 \bigg[ 1.06 \times 1.08 \bigg]$

$\qquad \longmapsto \sf Amount = 25,00 \times 1.448$

$\qquad \longmapsto \frak{\underline{\purple{\:Amount = Rs.2862 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:The \:Amount \:\:is\:\bf{Rs.2862}}}}$

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⠀⠀⠀⠀⠀Finding Compound- Interest :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Compound \:Interest \:: Amount- Principal}\bigg\rgroup$

⠀⠀⠀⠀⠀Here Principal is Rs. 2,500 & Amount is Rs. 2,862 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf Compound \: Interest \:: 2862 - 2500$

$\qquad \longmapsto \frak{\underline{\purple{\:Compound \:Interest\;= Rs.362 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:The \:Compound \:Interest \:\:is\:\bf{Rs.362}}}}$

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