CAT 2023 Slot 1 · Quant · Question 16

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

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

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

He then reinvests that whole amount for one year at 10% simple interest, 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, leaving 1.1P=22000\times{\left( 1.02 \right)}^{2}.

Since {\left( 1.02 \right)}^{2}=1.0404, this gives P=\frac{22000}{1.1}\times 1.0404=20000\times 1.0404.

So P=20808, that is ₹20808.

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 and the factor 1.1 survive.