CAT 2025 Slot2 Quant: A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594,

Method: Present Value Equivalence
The loan amount must be equal to the sum of the present values of the installments.
Let the multiplying factor be $k = (1 + \frac{r}{100})$.
$$1000 = \frac{530}{k} + \frac{594}{k^2}$$ Multiply by $k^2$:
$1000k^2 - 530k - 594 = 0$
$500k^2 - 265k - 297 = 0$
Solving for $k$ using the quadratic formula or substituting options:
For $k = 1.08$:
$500(1.1664) - 265(1.08) - 297 = 583.2 - 286.2 - 297 = 0$.
Since $k = 1.08$, the rate is $\mathbf{8\%}$.