Question

find the compound interest on rs 8000 for 1 year at 5 % p.a., compounded half yearly.​

Answer 1

Given:-

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• Principal (P) = Rs.8000

• Rate of interest (R) = 5 %

• Time (n) = 1 year

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To find:-

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• Find the compound interest

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Solution:-

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We know that,

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⠀⠀⠀⠀$\begin{gathered}\boxed{\sf{Amount= P(1 + \dfrac{R}{100})^{n}}} \\ \\ \end{gathered}$

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Where,

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• P = Principal

• R = Rate of interest

• n = time taken

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$\sf{:\implies Amount=8000(1+\dfrac{5}{2×100})^{2}}$

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$\sf{:\implies Amount=8000(1+\dfrac{1}{2×20})^{2}}$

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$\sf{:\implies Amount=8000(1+\dfrac{1}{40})^{2}}$

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$\sf{:\implies Amount=8000(\dfrac{41}{41})^{2}}$

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$\sf{:\implies Amount=8000×\dfrac{41}{40}×\dfrac{41}{40}}$

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$\sf{:\implies Amount=41×41×5}$

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$\sf{:\implies Amount=8405}$

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Now,

we also know that,

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$\boxed{\bf{\purple{Compound\:interest=Amount-Principal}}}$

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$\sf{:\implies Compound\:interest=8405-8000}$

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$\sf{:\implies Compound\:interest=Rs.405}$

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.°. the compound interest is Rs.405

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