Question

the sum of money lent at compound interest yields rupees 100 at the end of 1st year rupees 105 at the end of second year find rate of interest per annum

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{First year interset is Rs.100}\\\textsf{Second year interest is Rs.105}$

$\underline{\textsf{To find:}}$

$\textsf{The rate of interest}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the principal be P and rate of interet be r}$

$\textsf{For one year, both S.I and C.I are same}$

$\textsf{First year interest =Rs.100}$

$\implies\mathsf{\dfrac{Pnr}{100}=100}$

$\implies\mathsf{\dfrac{P{\times}1{\times}r}{100}=100}$

$\implies\mathsf{\dfrac{Pr}{100}=100}$

$\implies\mathsf{Pr=10000}$.........(1)

$\textsf{Then, Second year principal is P+100}$

$\textsf{Second year interest = Rs.105}$

$\implies\mathsf{\dfrac{(P+100){\times}1{\times}r}{100}=105}$

$\implies\mathsf{\dfrac{(P+100)r}{100}=105}$

$\implies\mathsf{(P+100)r=10500}$

$\implies\mathsf{Pr+100r=10500}$

$\implies\mathsf{10000+100r=10500}\;\;\;\textsf{(Using (1))}$

$\implies\mathsf{100r=10500-10000}$

$\implies\mathsf{100r=500}$

$\implies\mathsf{r=\dfrac{500}{100}}$

$\implies\boxed{\mathsf{r=5\,\%}}$

$\underline{\textsf{Answer:}}$

$\mathsf{Rate\;of\;interest\;is\;5\,\%}$

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