Question

STD 8

Find the difference between simple of interest and compound interest on Rs 4000 at 10% for 2 years​

Answer 1

Answer:

P=4000,r=10%,n=2years. On Calculation A we get, A=P(1+r100)n⇒A=4000(1+10100)2⇒A=P(1+110)2⇒A=4000(1110)2⇒A=4000×121100⇒A=4840 Rs. Hence the amount after 2 years will be 4840 and it'll only work as the principal amount for simple interest.

Step-by-step explanation:

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Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf \implies Principal = Rs. \: 4000$

$\sf \implies Rate = 10 \: \%$

$\sf \implies Time = 2 \: years$

$\bf \: \underline{To \: find} :$ ↴

$\sf \implies Compound \: interest - Simple \: interest = \: ?$

$\bf \: \underline{\underline{Solution}}$

$\sf \: First \: of \: all, let's \: find \: the \: value \: of \: (S.I) \: Simple \: interest.$

$\sf \implies \boxed{ \sf \: \pink{S.I = \dfrac{Principal \times Rate \times Time }{100} }}$

$\sf \implies\sf \:S.I = \dfrac{4000 \times 10 \times 2 }{100}$

$\sf \implies\sf \:S.I = \dfrac{40\!\!\!\not0\!\!\!\not0 \times 10 \times 2 }{1\!\!\!\not0\!\!\!\not0}$

$\sf \implies\sf \:S.I = 40 \times 10 \times 2$

$\red{\sf \implies\sf \: S.I = Rs. \: 800}$

$\sf \: Now, we \: will \: find \: the \: value \: of \: (C.I) \: Compound \: interest.$

$\sf \: For \: that, we \: have \: \: to \: find \: the \: amount.$

$\sf \implies \boxed{ \sf \: \pink{Amount = P \bigg( 1 + \dfrac{R }{100} \bigg)^{n} }}$

$\sf \implies \sf 4000 \bigg( 1 + \dfrac{10}{100} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg( 1 + \dfrac{1}{10} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg( \dfrac{10 + 1}{10} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg( \dfrac{11}{10} \bigg)^{2}$

$\sf \implies \sf 4000 \times \dfrac{121}{100}$

$\sf \implies \sf 40 \times 121$

$\red{\sf \implies \sf Amount = Rs. \: 4840}$

$\sf \: Now, Compound \: interest = Amount - Principal$

$\sf \implies \sf Rs. \: 4840 \: - \: Rs. \: 4000$

$\red{\sf \implies \sf Compound \: interest = Rs. \: 840}$

$\sf \: Now, difference \: between \: C.I \: and \: S.I \: is :$

$\sf \implies \sf Compound \: interest \: - \: Simple \: interest$

$\sf \implies \sf Rs. \: 840 \: - \: Rs. \: 800$

$\red{\sf \implies \sf Rs. \: 40}$

$\underline{ \boxed{ \pink{ \sf \: Hence, the \: difference \: between \: C.I \: and \: S.I = Rs. \: 10}}}$