CAT 2024 Slot 3 QA Question & Solution

ArithmeticMedium

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 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

Solution

Let us assume the amount invested to be $P$, and the rate of interest to be $r$.
Value of the investment after 3 years will be, $P\left(1+r\right)^3$
Value of the investment after 5 years will be, $P\left(1+r\right)^5$

$\left(1+r\right)^2=\frac{36}{25}$
$\left(1+r\right)^2=1.44$
$r=0.2$

We need to find the value of n for which $4000\left(1+r\right)^n>20000$
$\left(1+r\right)^n>5$
$\left(1.2\right)^n>5$
We see that,
$1.2^8=4.2999$
$1.2^9=5.15$

Hence it takes 9 years to grow to over 20,000.