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​

Answer 1

Given :

• P = Rs 8,000,

• R = 10% p.a. = 5% half yearly

• Time = 18 months = 3 half years.

Interest for the first half year

= 8000 x 5 x 1/100

= Rs 400

So, amount at the end of first half year

= 8000 + 400

= Rs 8400

So, principal for the second half year = Rs 8400

Interest for the second half year

= 8400 x 1 x 5/100

= Rs 420

Amount at the end of second half year

= Rs(8400 + 420)

= Rs 8820

Principal for the third half year = 8820

Interest for the third half year

= 8820 x 1 x 5/100

= Rs 441

Amount at the end of third year

= 8820 + 441

= Rs 9261

Compound interest

= 9261 - 8000

= Rs 1261

Simple interest = P x R x T/100

= 8000 x 10 x 1.5/100

= Rs 1200

Difference between SI and CI

= 1261 - 1200

= Rs 61

Answer 2

Answer:

• Simple Interest : This Interest on Principal, no Matter how many Years.
• Compound Interest : This Interest on Principal & Interest of Each Consecutive years.

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

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

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

• when Amount compounded Half Yearly, then we Reduce Rate by Half and Increase Time by Twice.
• In 1st Line it's Normal Interest for all 3 years.
• In 2nd Line it's Interest of Interest of 1st and (1st + 2nd) year respectively.
• In 3rd Line it's Interest of Interest.

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

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

$\rule{180}{1.5}$

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

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

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