CAT 2025 Slot 2 QA Question & Solution
ArithmeticMedium
Question
A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is
Options
10
11
9
8
Solution
Let the annual interest rate be (r) (in decimal). Discount the two instalments to present value:
$$\dfrac{530}{1+r}+\dfrac{594}{(1+r)^2}=1000$$
Set $$x=\dfrac{1}{1+r}$$. Then
$$594x^2+530x-1000=0$$
Discriminant = $$530^2+4\cdot594\cdot1000=280900+2376000=2656900=1630^2$$.
$$x=\dfrac{\ -b\pm\sqrt{b^2-4ac}}{2a}$$
$$x=\dfrac{-530+1630}{2\cdot594}=\frac{1100}{1188}=\dfrac{275}{297}$$
So $$1+r=\dfrac{297}{275}$$
$$r=\dfrac{297-275}{275}=\dfrac{22}{275}=\dfrac{2}{25}=0.08=8\%$$