Question

Find the difference between the simple interest and the compound interest on Rs. 8000 at 10% per annum for 3 years.

Answer 1

✬ Difference = Rs 248 ✬

Step-by-step explanation:

Given:

• Principal (P) is Rs 8000.
• Rate (R) is 10% per annum.
• Time (T) is 3 years.

To Find:

• What is the difference between Simple and compound interest ?

Solution: Here ,

• P = Rs 8000
• R = 10%
• T = 3 years

Formula for S.I is

★ S.I = P $\times$ R $\times$ T/100 ★

$\implies{\rm }$ 8000 $\times$ 10 $\times$ 3/100

$\implies{\rm }$ 80 $\times$ 10 $\times$ 3

$\implies{\rm }$ 2400

So, S.I is Rs 2400.

Now, for compound interest formula is

★ A = P ( 1 + R/100)^n ★

$\implies{\rm }$ A = 8000 (1 + 10/100)³

$\implies{\rm }$ 8000( 100 + 10/100)³

$\implies{\rm }$ 8000 (110/100)³

$\implies{\rm }$ 8000(11/10)³

$\implies{\rm }$ 8000 $\times$ 1331/1000

$\implies{\rm }$ 8 $\times$ 1331

$\implies{\rm }$ 10648

∴ C.I = Amount – Principal

➮ C.I = Rs (10648 – 8000)

➮ Rs 2648

Then ,Difference between S.I and C.I is

=> C.I – S.I

=> 2648 – 2400

=> Rs 248

Answer 2

$\bigstar$ $\sf{\orange{\underline{\underline{\green{To\:Find:-}}}}}$

• The difference between the simple interest and compound interest .

$\bigstar$ $\sf{\blue{\underline{\underline{\purple{SOLUTION:-}}}}}$

☞ GIVEN :-

• Principle (P) = Rs. 8000

• Rate (R) = 10%

• Time (T) = 3 years

☞ FORMULA :-

1) $\checkmark\:\tt{\underline{\green{\boxed{Amount(A)\:=\:P\:(1\:+\:{\dfrac{R}{100}})^t\:}}}}$

2) $\checkmark\:\tt{\underline{\blue{\boxed{Compound\:interest\:=\:Amount(A)\:-\:Principle(P)\:}}}}$

3) $\checkmark\:\tt{\underline{\red{\boxed{Simple\:interest\:=\:{\dfrac{PTR}{100}}\:}}}}$

☞ CALCULATION :-

1) $\tt{\implies\:Amount(A)\:=\:8000\:(1\:+\:{\dfrac{10}{100}})^3\:}$

$\tt{\implies\:A\:=\:8000\times(1.1)^3\:}$

$\tt{\implies\:A\:=\:8000\times{1.331}\:$

$\tt{\implies\:A\:=\:10648\:}</p><p></p><p>2) [tex]\tt{\implies\:compound\:interest\:=\:A\:-\:P\:}$

$\tt{\implies\:Compound\:interest\:=\:10648\:-\:8000\:}$

$\tt{\implies\:Compound\:interest\:=\:2648\:}$

3) $\tt{\implies\:Simple\:interest\:=\:{\dfrac{PTR}{100}}\:}$

$\tt{\implies\:Simple\:interest\:=\:{\dfrac{8000\times{3}\times{10}}{100}}\:}$

$\tt{\implies\:Simple\:interest\:=\:2400\:}$

☞ Now, difference between C.I and S.I .

$\tt{(Compound\:interest)\:-\:(Simple\:interest)\:}$

$\tt{\:=\:2648\:-\:2400\:}$

$\tt{\:=\:248\:}$