Question

1. Calculate the difference between the simple
interest and the compound interest on 4,000
in 2 years at 8% per annum compounded yearly.​

Answer 1

$\bf \: \underline{Given} :$ ↴

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

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

$\sf \implies Rate = 8 \: \%$

$\bf \: \underline{To \: find} :$ ↴

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

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

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

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

$\sf \implies\sf \:S.I = \dfrac{4000 \times 8 \times 2 }{100}$

$\sf \implies\sf \:S.I = \dfrac{40\!\!\!\not0\!\!\!\not0 \times 8 \times 2 }{1\!\!\!\not0\!\!\!\not0}$

$\sf \implies\sf \:S.I = 40 \times 8 \times 2$

$\red{\sf \implies\sf \:S.I = Rs. \: 640}$

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

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

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

$\sf \implies \sf 4000 \bigg( 1 + \dfrac{8 }{100} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg( 1 + \dfrac{2}{25} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg(\dfrac{25 + 2}{25} \bigg)^{2}$

$\sf \implies \sf 4000 \bigg(\dfrac{27}{25} \bigg)^{2}$

$\sf \implies \sf 4000 \times \dfrac{729}{625}$

$\sf \implies \sf 32 \times \dfrac{729}{5}$

$\sf \implies \sf \dfrac{23328}{5}$

$\red{\sf \implies \sf Amount = Rs. 4665.6}$

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

$\sf \implies \sf Rs. \: 4665.6 \: - \: Rs. \: 4000$

$\red{\sf \implies \sf Compound \: interest = Rs. \: 665.6}$

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

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

$\sf \implies \sf Rs. \: 665.6 \: - \: Rs. \: 640$

$\red{\sf \implies \sf Rs. \: 25.6}$

$\underline{ \boxed{ \pink{ \sf \: Hence, the \: difference \: between \: C.I \: and \: S.I = Rs. \: 25.6}}}$

Answer 2

Given :

• Principal (P) = Rs.4000
• Time (T) = 2 years
• Rate (R) = 8%

To Find :

• Difference between the simple interest And compound interest

Solution :

Simple interest = P × R × T/100

⟿ Simple interest = 4000 × 2 × 8/100

⟿ Simple interest = 8000 × 8/100

⟿ Simple interest = 64000/100

⟿ Simple interest = Rs. 640

Compound interest = P (1 + R/100)ⁿ - P

⟿ C.I = 4000 (108/100)2 - 4000

⟿ C.I = 4000 × 108/100 × 108/100 - 4000

⟿ C.I = 432 × 108/10 - 4000

⟿ C.I = 46656/10 - 4000

⟿ C.I = 4665.6 - 4000

⟿ C.I = Rs. 665.6

Difference between S.I And C.I

Compound interest - Simple interest

⟿ 665.6 - 640

⟿ Rs.25.6

Therefore,

Difference between S.I And C.I is Rs.25.6.