Question

Page Nou
The difference between the compound Interest and
simple Interest on a Principal P is placed at 7%
P.a . compounded annually for 2 years is a 490 then
Principal p is rs?
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Answer 1

Let Principal be Rs P

Time (n) = 2 years

Rate of interest, r = 7% per annum

We know,

Compound interest on Rs P for n years at the rate of r% per annum compounded annually is given by

$\tt{\implies CI=P\bigg(1+\dfrac{r}{100}\bigg)^{n}-P}$

and

Simple Interest on Rs P for n years at the rate of r% per annum is given by

$\tt{\implies SI=\dfrac{P \times r \times n}{100}}$

According to statement

$\rm :\longmapsto\:CI - SI = 490$

$\rm :\longmapsto\:P\bigg(1+\dfrac{r}{100}\bigg)^{n}-P - \dfrac{Prn}{100} = 490$

$\rm :\longmapsto\:P\bigg(1+\dfrac{7}{100}\bigg)^{2}-P - \dfrac{P \times 2 \times 7}{100} = 490$

$\rm :\longmapsto\:P\bigg(\dfrac{100 + 7}{100}\bigg)^{2}-P - \dfrac{14P}{100} = 490$

$\rm :\longmapsto\:P\bigg(\dfrac{107}{100}\bigg)^{2}-P - \dfrac{14P}{100} = 490$

$\rm :\longmapsto\:P(1.07)^{2} -P - \dfrac{14P}{100} = 490$

$\rm :\longmapsto\:P(1.1449) -P - 0.14P = 490$

$\rm :\longmapsto\:P(1.1449 - 1 - 0.14) = 490$

$\rm :\longmapsto\:P(0.0049) = 490$

$\rm :\longmapsto\:P = \dfrac{490}{0.0049}$

$\bf\implies \:P = 100000$

Additional Information :-

Compound interest on Rs P for n years at the rate of r% per annum compounded half yearly is given by

$\tt{\implies CI=P\bigg(1+\dfrac{r}{200}\bigg)^{2n}-P}$

Compound interest on Rs P for n years at the rate of r% per annum compounded quarterly is given by

$\tt{\implies CI=P\bigg(1+\dfrac{r}{400}\bigg)^{4n}-P}$