Question

Find the difference between compounds interest and simple interest for rs 7400 for 3years at 8%​

Answer 1

Given

• Principle , P = Rs. 7400
• Time , t = 3 years
• Rate of interest , R = 8 %

To find

● Difference between the Compound interest and Simple interest

Formula used

▶ Formula for calculating Simple interest (S.I.)

$\boxed{\sf{S.I.= \frac{P\times R \times t}{100}}}$

(where P is the principle , R is the rate of interest , t is the time )

▶ Formula for calculating Compound interest (C.I.)

$\boxed{\sf{C.I.=P\left( 1+\frac{R}{100}\right)^{t}-P}}$

(where P is the principle , R is the rate of interest , t is the time)

Solution

Calculating S.I.

$\implies\sf{S.I.=\frac{7400\times8\times3}{100}}$

$\implies\underline{\underline{\sf{S.I.=1776\;\;Rs}}}$

Calculating C.I.

$\implies\sf{C.I.=7400\left(1+\frac{8}{100}\right)^3-7400}$

$\implies\sf{C.I.=7400\left((1+\frac{8}{100})^3-1\right)}$

$\implies\sf{C.I.=7400\left(1+\frac{512}{1000000}+\frac{24}{100}(1+\frac{8}{100})-1\right)}$

$\implies\sf{C.I.=7400\left(\frac{512}{1000000}+\frac{24}{100}+\frac{192}{10000}\right)}$

$\implies\sf{C.I.=7400\left(\frac{512+240000+19200}{1000000}\right)}$

$\implies\sf{C.I.=7400\times\frac{259712}{1000000}}$

$\implies\underline{\underline{\sf{C.I.=1921.8\;\;Rs}}}$

Finding the difference b/w C.I. and S.I.

$\longmapsto\sf{C.I.-S.I.=1921.8-1776}$

$\longmapsto\underline{\boxed{\sf{C.I.-S.I.=145.8\;\;Rs}}}$

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \purple{Question:-}}}}}}$

▪ Find the difference between compound interest and simple interest on Rs. 7400 for 3 years at 8%.

${ \huge{ \bold{ \underline{ \underline{ \purple{S olution: -}}}}}}$

${ \bold{ \underline{ \red{given-}}}}$

▪ Principal = P = Rs. 7,400

▪ Rate = R = 8 %

▪ Time = T = 3 years

${ \bigstar \: \: { \underline{ \bold{ \pink{compound \: interest}}}}}$



${ \boxed{ \boxed{ \bold{ \red{C.I . = P( {(1 + \frac{R}{100} )}^{T} - 1)}}}}}$



${ \bold{ \implies{C.I. = 7400( {(1 + \frac{8}{100}) }^{3} - 1)}}}$



${ \bold{ \implies{C .I. = 7400( {(1 + \frac{2}{25} )}^{3} - 1)}}}$



${ \bold{ \implies{C .I. = 7400( ({ \frac{27}{25}) }^{3} - 1)}}}$



${ \bold{ \implies{C .I. = 7400( \frac{19683}{15625} - 1)}}}$



${ \bold{ \implies{C .I. = 7400 \frac{(19683 - 15625)}{15625} }}}$



${ \bold{ \implies{C.I . = 7400 \times \frac{4058}{15625} }}}$



${ \boxed{ \red{ \bold{compound \: interest =Rs. 1921.87}}}}$



${ \bigstar \: \: \: { \bold{ \underline{ \pink{simple \: interest}}}}}$



${ \boxed{ \boxed{ \bold{ \red{ \: \: \: S.I . = \frac{P \times R \times T}{100} \: \: \: \: }}}}}$



${ \bold{ \implies{S .I. = \frac{7400 \times 8 \times 3}{100} }}}$



${ \bold{ \implies{S .I. = 74 \times 8 \times 3}}}$



${ \boxed{ \bold{ \red{ \: simple \: interest = Rs. \: 1776 \: }}}}$



therefore,

☆ difference between compound interest and simple interest .....



${ \bold{ \orange{ = C .I. \: - \: S.I.}}}$



${ \bold{ = Rs. \: 1921.87 - \: Rs. \: 1776}}$



${ \bold{ \huge{ \red{ = Rs. \: 145.87}}}}$