Question

calculate the amount and th compound intrest on 8000 for 2 years 9 months at 10 % p.a , compounded annualy​

Answer 1

Given

• Principal(P) = Rs.8000
• Rate(R) = 10%
• Time(T) = 2 year's and 9 months

To Find

• Amount And Compund Interest

Formula

$\boxed{\gray{\sf~~~~~SI= \dfrac{Principal×Rate × Time}{100}}}$

$\boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}$

Solution

Principal(P) = Rs.8000

Rate(R) = 10%

Time(T) = 2 year's

Amount = ???

$\boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}$

Putting the values

${Amount = 8000\Bigg\{1 + \dfrac{10}{100}\Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{100 + 10}{100}\Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{110}{100}\Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$

${Amount = 8000 \times \dfrac{121}{100}}$

${Amount = 80 \times {121}}$

${Amount = 9680}$

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Simple Interest for 9 months

Principal(P) = Rs.8000

Rate(R) = 10%

Time(T) = 9 months = 9/12 Year's

Simple interest = ???

${\sf~~~~~SI= \dfrac{Principal×Rate × Time}{100}}$

${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$

${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$

${\sf~~~~~SI= 20 \times 90 }$

${\sf~~~~~SI= 1800 }$

Total Amount = 9680+1800

Total Amount = 11780

Compound interest = Amount - Principal

Compound interest = 11780-8000

Compound interest = 3780

• $\\ \\ \\ \boxed{ \bf\therefore Amount = 11780 \: \: \: \: \: \bf Compound \: \: Interest = 3780}$

$\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}$

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Answer 2

Given

• GivenPrincipal(P) = Rs.8000
• GivenPrincipal(P) = Rs.8000Rate(R) = 10%
• GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 months

GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 monthsTo Find

• GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 monthsTo FindAmount And Compund Interest

GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 monthsTo FindAmount And Compund InterestFormula

GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 monthsTo FindAmount And Compund InterestFormula$\boxed{\gray{\sf~~~~~SI= \dfrac{Principal×Rate × Time}{100}}}$

GivenPrincipal(P) = Rs.8000Rate(R) = 10%Time(T) = 2 year's and 9 monthsTo FindAmount And Compund InterestFormula$\boxed{\gray{\sf~~~~~SI= \dfrac{Principal×Rate × Time}{100}}}$$\boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}$

Solution

Principal(P) = Rs.8000

Rate(R) = 10%

Time(T) = 2 year's

Amount = ???

[tex] \boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}[/tex]

tex] \boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}[/tex]Putting the values

tex] \boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}[/tex]Putting the values${Amount = 8000\Bigg\{1 + \dfrac{10}{100}\Bigg\}^2}$

tex] \boxed{\gray{Amount = P\Bigg\{1 + \dfrac{R}{100}\Bigg\}^n}}[/tex]Putting the values${Amount = 8000\Bigg\{1 + \dfrac{10}{100}\Bigg\}^2}$${Amount = 8000\Bigg\{ \dfrac{100 + 10}{100}\</strong>Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{110}{100}\Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$${Amount = 8000 \times \dfrac{121}{100}}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$${Amount = 8000 \times \dfrac{121}{100}}$${Amount = 80 \times {121}}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$${Amount = 8000 \times \dfrac{121}{100}}$${Amount = 80 \times {121}}$${Amount = 9680}$

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$${Amount = 8000 \times \dfrac{121}{100}}$${Amount = 80 \times {121}}$${Amount = 9680}$______________

${Amount = 8000\Bigg\{ \dfrac{11}{10}\Bigg\}^2}$${Amount = 8000 \times \dfrac{121}{100}}$${Amount = 80 \times {121}}$${Amount = 9680}$______________Simple Interest for 9 months

Principal(P) = Rs.8000

Rate(R) = 10%

Time(T) = 9 months = 9/12 Year's

Simple interest = ???

${\sf~~~~~SI= \dfrac{Principal×Rate × Time}{<strong>100}}$

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$${\sf~~~~~SI= 20 \times 90 }$

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$${\sf~~~~~SI= 20 \times 90 }$${\sf~~~~~SI= 1800 }$

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$${\sf~~~~~SI= 20 \times 90 }$${\sf~~~~~SI= 1800 }$Total Amount = 9680+1800

100}}[/tex]${\sf~~~~~SI= \dfrac{8000 \times 10 \times 9 }{100 \times 4}}$${\sf~~~~~SI= \dfrac{8000 \times 90 }{400 }}$${\sf~~~~~SI= 20 \times 90 }$${\sf~~~~~SI= 1800 }$Total Amount = 9680+1800Total Amount = 11780

Compound interest = Amount - Principal

Compound interest = 11780-8000

Compound interest = 11780-8000Compound interest = 3780

Compound interest = 11780-8000Compound interest = 3780$\\ \\ \\ \boxed{ \bf\therefore Amount = 11780 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:</strong> \: \: \: \: \: \\ \bf Compound \: \: Interest = 3780}$