Simple Interest and Compound Interest Question 1 - CAT 2023
Anil borrows Rs. 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs. 10,320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to:
Step-by-Step Explanation
- Determine the effective rate and tracking timeline:
The nominal annual interest rate is 8%. Since compounding occurs half-yearly, the tracking period interest rate is:
Half-yearly rate = 8% / 2 = 4% (multiplier = 1.04)
- Track the loan balance at the end of Year 1:
One year consists of 2 half-yearly periods.
Balance before payment = 200,000 × (1.04)² = 200,000 × 1.0816 = Rs. 216,320
Anil pays back Rs. 10,320 at this point.
Outstanding Principal for Year 2 = 216,320 − 10,320 = Rs. 206,000
- Track the remaining balance to the end of Year 3:
The outstanding balance grows over the remaining 2 years (which equals 4 half-yearly periods):
Final Closing Payment = 206,000 × (1.04)⁴
Expanding the decimal factor:
(1.04)⁴ = (1.0816)² ≈ 1.16985856
Final Closing Payment ≈ 206,000 × 1.16985856 ≈ Rs. 240,990.87
- Calculate total interest paid:
Instead of adding separate internal interest tranches, sum the total money paid back by the borrower and subtract the original principal:
Total Paid Back = First Payment + Final Payment
Total Paid Back = 10,320 + 240,990.87 = Rs. 251,310.87
Total Interest Paid = 251,310.87 − 200,000 = Rs. 51,310.87 ≈ Rs. 51,311
Correct Option: B
💡 FundaMakers Tip:
When tracking dynamic multi-stage repayment schemes, do not calculate the interest earned period by period. It creates unnecessary math. Keep a simple ledger of absolute cash flows: Total Interest = (Sum of all payments made) − (Original Principal Borrowed). This macro view keeps your focus clear and lets you crack the final number in one step.