Question

Q.48) The compound interest of Rs .12,000 for 4 years at the rate 8%

p.a.is more than the simple interest on same amount for 4 years at the

rate 8% p.a. by Rs_______.

a) 485.87

b) 458.75

c) 487.54

d) 478.45​

Answer 1

$\textbf{Given:}$

$\textsf{Principal=Rs.12000}$

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

$\mathsf{Number\;of\;years=4}$

$\textbf{To find:}$

$\textsf{Difference between C.I and S.I}$

$\textbf{Solution:}$

$\underline{\textsf{Compund interest:}}$

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

$\mathsf{=12000\left(1+\dfrac{8}{100}\right)^4-12000}$

$\mathsf{=12000\left(\dfrac{108}{100}\right)^4-12000}$

$\mathsf{=12000\left(\dfrac{27}{25}\right)^4-12000}$

$\mathsf{=12000\left(\dfrac{27{\times}27{\times}27{\times}27}{25{\times}25{\times}25{\times}25}\right)-12000}$

$\mathsf{=480\left(\dfrac{27{\times}27{\times}27{\times}27}{25{\times}25{\times}25}\right)-12000}$

$\mathsf{=96\left(\dfrac{27{\times}27{\times}27{\times}27}{25{\times}25{\times}5}\right)-12000}$

$\mathsf{=16325.87-12000}$

$\mathsf{=Rs.\;4325.87}$

$\underline{\mathsf{Simple\;interest:}}$

$\mathsf{=\dfrac{P\;n\;r}{100}}$

$\mathsf{=\dfrac{12000{\times}4{\times}8}{100}}$

$\mathsf{=120{\times}4{\times}8}$

$\mathsf{=Rs.\;3840}$

$\underline{\mathsf{Difference\;between\;C.I\;and\;S.I}}$

$\mathsf{=4325.87-3840}$

$\mathsf{=Rs.485.87}$

$\textbf{Answer:}$

$\mathsf{Option\;(a)\;is\;correct}$

$\textbf{Find more:}$

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