Two Loan Offers and a Fee That Never Says Interest
Ravi runs a small wholesale shop and needs exactly ₹1,00,000 of working capital for one year, to buy stock he expects to resell at an 18% markup. Two offers are on the table. Offer A, from a fintech lender: 12% per annum simple interest, plus a processing fee of 2% of the sanctioned amount deducted from the disbursement, so ₹98,000 is credited to his account but ₹1,12,000 must be repaid at the end of the year. Offer B, from his bank: 10% per annum compounded half-yearly, no processing fee, the full ₹1,00,000 credited, and the entire principal plus interest repaid at the end of the year. Ravi's accountant argues that 12% simple is 'close enough' to 10% compounded and that the bank will take longer to sanction, so he advises Offer A. Ravi must decide today.
1. Compute the rupee cost of borrowing under each offer and the effective annual rate on the money Ravi actually gets to use. Which offer is cheaper, and by how much?
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Offer A. The fee is ₹2,000 (2% of ₹1,00,000) and is deducted upfront, so Ravi uses only ₹98,000. Simple interest = 1,00,000 × 12/100 = ₹12,000, but it is charged on the sanctioned amount, not on the ₹98,000 he received.
- Total outgo = 2,000 (fee) + 12,000 (interest) = ₹14,000
- Effective rate = 14,000 / 98,000 = 14.29% p.a.
Offer B. Half-yearly compounding at 10% p.a. means 5% every six months:
- Amount repayable = 1,00,000 × (1.05)² = 1,00,000 × 1.1025 = ₹1,10,250
- Total cost = ₹10,250
- Effective rate = 10,250 / 1,00,000 = 10.25% p.a.
Offer B is cheaper by ₹14,000 − ₹10,250 = ₹3,750, and the true gap is 14.29% versus 10.25% - over four percentage points, not the two points the accountant is comparing.
The trap is structural. A processing fee never appears in the 'rate', yet it raises the cost twice over: it is money paid, and it shrinks the base on which the effective rate is calculated. Comparing a simple rate with a compounded rate without converting both to an effective annual figure is the error that produced the accountant's advice.
2. The accountant says the two offers differ by only two percentage points and that the fee is a small price for speed. Quantify what the fee actually costs Ravi at the end of the year, using his 18% resale margin.
Read the worked answer
Trace the cash, not the rate.
Under Offer A: Ravi has ₹98,000 to buy stock. Selling at an 18% markup gives 98,000 × 1.18 = ₹1,15,640. He repays ₹1,12,000. Cash left = ₹3,640.
Under Offer B: Ravi has ₹1,00,000 to buy stock. Selling at 18% gives ₹1,18,000. He repays ₹1,10,250. Cash left = ₹7,750.
Difference in Ravi's pocket = ₹7,750 − ₹3,640 = ₹4,110, which is more than double.
Where does the ₹4,110 come from? Three stacked effects of the same ₹2,000 fee:
- He pays the ₹2,000 in cash.
- That ₹2,000 never buys stock, so it earns no margin: he forgoes 2,000 × 0.18 = ₹360 of profit.
- He still pays 12% interest on the full ₹1,00,000 sanctioned, not on the ₹98,000 he received - about ₹240 of interest charged on money he never held.
On top of that sits the ₹1,750 difference between 12% simple on ₹1,00,000 and 10% compounded half-yearly. Add them and the ranking is decisive.
The examinable habit: convert every offer into 'cash in hand at the end of the horizon' before comparing. Speed is worth something, but here it must be worth more than ₹4,110 on a one-year ₹1,00,000 decision before Offer A becomes rational.
3. Ravi negotiates the processing fee away, and the fintech then offers 12% per annum simple interest with no fee at all. At what simple rate would the two offers be financially identical, and does the negotiated offer change the recommendation?
Read the worked answer
Set the two rupee costs equal. Offer B costs ₹10,250 whatever happens, since it is untouched by the negotiation.
With no fee, Offer A costs only its simple interest, 1,00,000 × r/100. Setting 1,00,000 × r/100 = 10,250 gives r = 10.25% p.a. simple.
So:
- At 12% simple with no fee, Offer A costs ₹12,000 against ₹10,250 - still ₹1,750 worse. The negotiation removed ₹2,000 of fee but did not close the gap, because the fee was never the only defect.
- Offer A becomes the better deal only below 10.25% simple, i.e. roughly 2 percentage points below its current quote.
The number 10.25% is not a coincidence: it is the effective annual rate of 10% compounded half-yearly, since (1.05)² = 1.1025. That is the conversion a candidate must be able to do on sight - split the nominal rate into compounding periods and rebuild it. It also explains why the accountant's '2 percentage points' comparison is meaningless: 12% simple and 10% compounded half-yearly are not two points apart on a comparable basis, they are 12% versus 10.25% on the base rate alone, before the fee adds another three points.
Recommendation: Ravi should take Offer B. Speed is the only remaining argument for Offer A, and it now has to be worth ₹1,750 plus the sanction delay.