Question

1) Find the difference between simple interst and compoundinterest on Rs. 6250 in 2 years at 4 p.c.p.a.​

Answer 1

$\bf \: \underline{Given} :$ ↴

$\sf \implies Principal = Rs. \: 6250$

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

$\sf \implies Rate = 4 \: \%$

$\bf \: \underline{To \: find} :$ ↴

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

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

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

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

$\sf \implies\sf \:S.I = \dfrac{6250 \times 4 \times 2 }{100}$

$\sf \implies\sf \:S.I = \dfrac{625 \times 4 \times 2 }{10}$

$\sf \implies\sf \:S.I = \dfrac{625 \times 4 }{5}$

$\sf \implies\sf \:S.I = 125 \times 4$

$\red{\sf \implies\sf \: S.I = Rs. \: 500}$

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

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

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

$\sf \implies \sf 6250 \bigg( 1 + \dfrac{4 }{100} \bigg)^{2}$

$\sf \implies \sf 6250 \bigg( 1 + \dfrac{1}{25} \bigg)^{2}$

$\sf \implies \sf 6250 \bigg(\dfrac{25 + 1}{25} \bigg)^{2}$

$\sf \implies \sf 6250 \bigg(\dfrac{26}{25} \bigg)^{2}$

$\sf \implies \sf 6250 \times \dfrac{676}{625}$

$\sf \implies \sf 10 \times 676$

$\red{\sf \implies \sf Amount = Rs. \: 6760}$

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

$\sf \implies \sf Rs. \: 6760 \: - \: Rs. \: 6250$

$\red{\sf \implies \sf Compound \: interest = Rs. \: 510}$

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

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

$\sf \implies \sf Rs. \: 510 \: - \: Rs. \: 500$

$\red{\sf \implies \sf Rs. \: 10}$

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

Answer 2

Given :

• Principal (P) = Rs. 6250
• Rate (R) = 4%
• Time (T) = 2 years

To Find :

• Difference between simple interest And compound interest

Solution :

S.I = P × R × T/100

⟿ S.I = 6250 × 4 × 2/100

⟿ S.I = 25000 × 2/100

⟿ S.I = 50000/100

⟿ S.I = Rs. 500

C.I = P (1 + R/100)ⁿ - P

⟿ C.I = 6250 (1 + 4/100)² - 6250

⟿ C.I = 6150 × 104/100× 104/100 - 6250

⟿ C.I = 6250 × 104 × 104/10000 - 6250

⟿ C.I = 6260000/10000 - 6250

⟿ C.I = 6260 - 6250

⟿ C.I = Rs. 510

Difference between S.I And C.I

⟿ C.I - S.I

⟿ 510 - 500

⟿ Rs. 10

Difference between S.I And C.I is Rs. 10