CAT 2025 Slot 1 · Quant · Question 6

Under simple interest the amount grows by the same amount each year, so differences give the yearly interest directly.

Between 3 years and 6.5 years, that is 3.5 years, the amount grows by 18960-13920=5040. So one year's interest is \frac{5040}{3.5}=1440.

Three years of interest is 4320, so the principal is 13920-4320=9600, and the rate is \frac{1440}{9600}=15\% per annum.

Compounded half yearly, the rate per period is 7.5\% and 2 years is 4 periods

= 9600\times{\left( 1.075 \right)}^{4}=9600\times 1.33546\ldots =12820.50.

The interest is 12820.50-9600=3220.50, nearest to ₹3221.