CAT 2024 Slot 2 · Quant · Question 15

Half-yearly compounding at 4% per annum means 2% per half-year, with 2 periods a year.

Anil invests for 6 years, which is 12 half-years, so his amount is 22000\times{\left( 1.02 \right)}^{12}.

Sunil invests P for 5 years, which is 10 half-years, reaching P\times{\left( 1.02 \right)}^{10}.

That whole amount then earns 10% simple interest for one year, multiplying it by 1.1.

So Sunil's final amount is P\times{\left( 1.02 \right)}^{10}\times 1.1.

Setting the two equal, P\times{\left( 1.02 \right)}^{10}\times 1.1=22000\times{\left( 1.02 \right)}^{12}.

The common factor {\left( 1.02 \right)}^{10} cancels from both sides, leaving 1.1P=22000\times{\left( 1.02 \right)}^{2}.

So P=\frac{22000}{1.1}\times 1.0404=20000\times 1.0404.

That is P=20808, that is ₹20808, the second option.

Shortcut. Never expand {\left( 1.02 \right)}^{12}. The two investments share ten of the twelve half-yearly periods, so those cancel and only the extra two half-years, {\left( 1.02 \right)}^{2}=1.0404, and the factor 1.1 survive.