Question

the difference between simple interest and compound interest at the rate of 10% for two years on an amount is rs. 20 find the principle value​

Answer 1

Step-by-step explanation:

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Answer 2

⇒ Given:

The difference between simple interest and compound interest at the rate of 10% for two years on an amount is rs.20.

⇒ To Find:

The principal amount.

⇒ Solution:

We have to solve the simple and compound interest values separately.

Let's assume the value of principal amount as "p".

$\sf{\implies\:Simple\:Interest}$

Formula used:

$\sf{\maltese\:S.I=\dfrac{PRT}{100}}$

It is given that:

✳ Rate of interest = 10%

✳ Time = 2 years

Substituting these values in the equation:

$\sf{\longrightarrow\:S.I=\dfrac{P\times10\times2}{100}}$

$\sf{\longrightarrow\:S.I=\dfrac{20p}{100}}$

The simple interest is 20p/100.

$\sf{\implies\:Compound\:Interest}$

Formula used:

$\sf{\maltese\:Compound\:Interest=Amount-Principal}$

Writing the formula in equational format:

$\sf{\maltese\:C.I=P(1+\dfrac{r}{100})^n-p}$

It is given that:

✳ Rate of interest = 10%

✳ Time = 2 years

Substituting these values in the equation:

$\sf{\longrightarrow\:C.I=P(1+\dfrac{10}{100})^2-p}$

$\sf{\longrightarrow\:C.I=P(1+\dfrac{1}{10})^2-p}$

$\sf{\longrightarrow\:C.I=\dfrac{121p}{100}-p}$

$\sf{\longrightarrow\:C.I=\dfrac{21p}{100}}$

The compound interest is 21p/100.

Now, it is given that:

$\sf{\implies\:C.I-S.I=Rs.20}$

Substituting the values in the equation:

$\sf{\longrightarrow\dfrac{21p}{100}-\dfrac{20p}{100}=20}$

$\sf{\longrightarrow\dfrac{p}{100}=20}$

$\sf{\longrightarrow\:p=20\times100}$

$\sf{\longrightarrow\:p=Rs.2000}$

The principal amount is Rs. 2000.