CAT 2023 Slot 2 · Quant · Question 12

Half-yearly compounding at 8% per annum means 4% per half-year.

After one year, that is two half-yearly periods, the debt grows to 200000\times{\left( 1.04 \right)}^{2}.

Since {\left( 1.04 \right)}^{2}=1.0816, the debt stands at 200000\times 1.0816=216320.

Anil repays ₹10320 at this point, leaving 216320-10320=206000 outstanding.

This balance then compounds for two more years, that is four more half-yearly periods.

So the closing payment is 206000\times{\left( 1.04 \right)}^{4}.

Now {\left( 1.04 \right)}^{4}={\left( 1.0816 \right)}^{2}\approx 1.16986.

The closing payment is therefore about 206000\times 1.16986\approx 240991.

The total of all repayments is 10320+240991=251311.

The interest is the excess over the amount borrowed: 251311-200000=51311 — the second option.

Shortcut. The repayment of ₹10320 is suspiciously close to the first year's interest of ₹16320, but it is less, so the balance stays above the original principal at ₹206000. That alone rules out option 3, and since {1.04}^{4} is roughly 1.17, the final payment is near ₹241000 — only option 2 is in range.