CAT 2025 Slot 2 · Quant · Question 18

Let the rate be r as a decimal.

After one year the debt grows to 1000\left( 1+r \right), and paying 530 leaves 1000\left( 1+r \right)-530.

That balance grows by another factor \left( 1+r \right) and is cleared by the second payment, so \left[ 1000\left( 1+r \right)-530 \right]\left( 1+r \right)=594.

This is a quadratic, but the options are clean percentages, so substituting is faster than expanding.

At r=0.08: 1000\times 1.08=1080, and paying 530 leaves a balance of 550.

Carrying that forward, 550\times 1.08=594, which matches the second installment exactly.

So the rate of interest is 8%.

Shortcut. The second installment, 594, must be the year-1 balance multiplied by \left( 1+r \right). Since 594=2\times{3}^{3}\times 11, the factor \left( 1+r \right) has to divide 594 neatly — and \frac{594}{1.08}=550 is a round number, while 1.09, 1.10 and 1.11 are not. Checking 8% first is the quickest route.