Question

Find the time in which Rs.12500 will produce Rs.3246.40 as compound Interest at 8% per annum, compounded annually.

Answer 1

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

$\textsf{Principal, P= Rs.12500}$

$\mathsf{Rate\;of\;interest,\;r=8\%}$

$\mathsf{Interest=Rs.3246.40}$

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

$\textsf{Number of years}$

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

$\textsf{We apply compound interest formula}$

$\boxed{\mathsf{Compound\;interest=P\left(1+\dfrac{r}{100}\right)^n-P}}$

$\implies\mathsf{3246.40=12500\left(1+\dfrac{8}{100}\right)^n-12500}$

$\implies\mathsf{3246.40+12500=12500\left(1+\dfrac{2}{25}\right)^n}$

$\implies\mathsf{15746.40=12500\left(1+\dfrac{2}{25}\right)^n}$

$\implies\mathsf{\dfrac{15746.40}{12500}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\dfrac{157464}{125000}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\dfrac{78732}{62500}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\dfrac{39366}{31250}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\dfrac{19683}{15625}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\dfrac{27{\times}27{\times}27}{25{\times}25{\times}25}=\left(\dfrac{27}{25}\right)^n}$

$\implies\mathsf{\left(\dfrac{27}{25}\right)^3=\left(\dfrac{27}{25}\right)^n}$

$\textsf{Equating powers on bothsides, we get}$

$\mathsf{n=3}$

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

$\textsf{The required time is 3 years}$

$\underline{\textsf{Find more:}}$

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Answer 2

Hope it helps you...Thank you