CAT 2021

Slot 1

QA

Question & Solution

Let the principal amount be P and the interest rate be r.

Then $P\left(1+r\right)^2-P\left(1+r\right)=806.25$ -(1)

$P\left(1+r\right)^3-P\left(1+r\right)^2=866.72$ -(2)

Dividing (2) by (1), we get:

$\frac{\left(P\left(1+r\right)^3-P\left(1+r\right)^2\right)}{P\left(1+r\right)^2-P\left(1+r\right)}=\frac{866.72}{806.25}$

$\frac{\left(\left(1+r\right)^2-1-r\right)}{1+r-1}=1.075$

$\frac{r^2+r}{r}=1.075$

r=0.075 or 7.5%

$\frac{\left(Interest\ accrued\ in\ 4th\ yr\right)}{Interest\ accrued\ in\ 3rd\ yr}=\frac{X}{866.72}$

$\frac{\left(P\left(1+r\right)^4-P\left(1+r\right)^3\right)}{P\left(1+r\right)^3-P\left(1+r\right)^2}=\frac{X}{866.72}$

Dividing numerator and denominator by $P\left(1+r\right)^2$

$\frac{r^2+2r+1-1-r}{1+r-1}=\frac{X}{866.72}$

$r+1=\frac{X}{866.72}$

$X=1.075\times\ 866.72=931.72$