Question

find the difference between the SI and CI on 8000 for 1.5 years at 10% per annum compound interest being compounded half yearly

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Answer 1

Answer:

S.I = 1200

Step-by-step explanation:

Answer 2

Step-by-step explanation:

$\underline{\:\large{\textit{1. \sf Simple Interest :}}}$

$:\implies\sf Simple\:Interest=\dfrac{Principal \times Rate \times Time}{100}\\\\\\:\implies\sf SI = \dfrac{8000 \times 10 \times 1.5}{100}\\\\\\:\implies\sf SI = 80 \times 15\\\\\\:\implies\sf SI = Rs.\:1200$

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$\underline{\:\large{\textit{2. \sf Compounded Half Yearly :}}}$

$\frak{Given}\begin{cases}\textsf{Principal = Rs. 8000}\\\textsf{Rate = \frac{10}{2} = 5\%}\\\textsf{Time = 1.5 \times 2 = 3}\end{cases}\\\begin{array}{|c|c|c|}\cline{1-3}\textit{1\sf st year}&\textit{2\sf nd year}&\textit{3\sf rd year}\\\cline{1-3}&&\\\sf8000\times\dfrac{5}{100} = 400&\sf8000\times\dfrac{5}{100} = 400&\sf8000\times\dfrac{5}{100} = 400&&&\\\cline{1-3}&&\\&\sf400\times\dfrac{5}{100} = 20&\sf2 \times 400\times\dfrac{5}{100} = 40&&&\\\cline{1-3}&&\\&&\sf20\times\dfrac{5}{100} = 1&&&\\\cline{1-3}\end{array}$

$:\implies\sf CI=(400+400+400)+(20+40)+1\\\\\\:\implies\sf CI = 1200 + 60 + 1\\\\\\:\implies\sf CI = Rs.\:1261$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Difference b/w CI and SI :}}$

$\dashrightarrow\sf Difference=Compound\:Interest-Simple\:Interest\\\\\\\dashrightarrow\sf Difference=Rs.\:1261-Rs.\:1200\\\\\\\dashrightarrow\underline{\boxed{\sf Difference=Rs.\:61}}$

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$\therefore\:\underline{\textsf{Difference b/w CI \& SI is \textbf{Rs. 61}}}.$