CAT 2024 Slot 3 QA Question 9: Aman invests Rs $4000$ in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after $3$ years to the value of the investment after $5$ years is $25:3

Question

Aman invests Rs $4000$ in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after $3$ years to the value of the investment after $5$ years is $25:3

Accepted Answer

Let the annual growth factor be $k$.

$\dfrac{4000k^{3}}{4000k^{5}} = \dfrac{25}{36}$
$\dfrac{1}{k^{2}} = \dfrac{25}{36}$
$k = \dfrac{6}{5}$

We need the smallest integer $n$ such that the investment exceeds Rs $20000$.

$4000(\dfrac{6}{5})^{n}>20000$
$(\dfrac{6}{5})^{n}>5$

$(\dfrac{6}{5})^{8}\appr