Flat 9% or Reducing 12%?
A shop owner needs ₹5,00,000 for 24 months to buy a delivery vehicle. Two lenders quote as follows.
Offer P: flat rate of 9% per annum, repayable in 24 equal monthly instalments on the full amount borrowed, with a processing fee of 1% of the sanction, deducted upfront from the disbursement.
Offer Q: 12% per annum on a reducing balance, repayable in 24 equal monthly instalments, with a flat processing fee of ₹2,000, also deducted upfront.
The owner's agent recommends Offer P: "Nine per cent is obviously cheaper than twelve per cent, and a flat rate is simpler." The owner is unsure, because the fee on P reduces the money he actually gets to use, and the instalments are equal in both cases.
You are asked to compare the two offers on total cash outflow and on how much money the borrower actually receives, and to test how far the flat rate would have to fall before P becomes the cheaper choice.
1. Compute the total cash outflow and the net amount received under each offer, and state which offer is cheaper.
Read the worked answer
Offer P (flat): interest = 5,00,000 × 9% × 2 = ₹90,000. Total repayment = ₹5,90,000, so EMI = 5,90,000 ÷ 24 = ₹24,583 (approx). The 1% fee of ₹5,000 is deducted upfront, so the borrower receives only ₹4,95,000 but repays ₹5,90,000.
Offer Q (reducing): monthly rate 1%, n = 24. EMI = 5,00,000 × 0.01 × (1.01)^24 ÷ [(1.01)^24 − 1] ≈ ₹23,537. Total repayment = 23,537 × 24 ≈ ₹5,64,888; add the ₹2,000 fee → ₹5,66,888, on a full ₹5,00,000 disbursal.
Decision: including fees, P costs ₹5,95,000 against Q's ₹5,66,888 - Q is cheaper by about ₹28,112, and it also puts ₹5,000 more usable money in the borrower's hands. The nominal 9% is misleading: a two-year flat rate translates to roughly 16.4% per annum on a reducing balance, so P is the costlier loan even though its headline number is smaller.
2. What flat rate would make Offer P as cheap as Offer Q on total cash outflow (fees included)? Would simply waiving P's processing fee close the gap?
Read the worked answer
Set P's total cash paid equal to Q's: 5,00,000 + interest + 5,000 = 5,66,888, so interest must be ₹61,888 or less.
For a flat loan, interest = principal × rate × 2 = 5,00,000 × r × 2. Hence r ≤ 61,888 ÷ 10,00,000 = 6.19% per annum (roughly 6.2%).
Waiving the fee alone does not close the gap: it saves only ₹5,000, while P is ₹28,112 more expensive overall. Even with a zero fee, P's total would be ₹5,90,000, still about ₹23,112 above Q. In other words, the fee explains only a small part of the disadvantage; the flat-rate structure explains the rest. This is the standard trap in loan comparisons - the fee and the quoting convention must both be converted to the same basis before any rate comparison is valid.
3. The owner can negotiate only one term. What single change to Offer P would actually beat Offer Q, and what change would not?
Read the worked answer
Only a cut in the flat rate works. Reducing the flat rate to about 6.19% (or below) brings P's total cash outflow down to Q's level; below that, P wins outright.
Changes that would not be enough:
- Waiving the ₹5,000 processing fee (saves ₹5,000 against a ₹28,112 gap).
- Extending the tenure of P's flat loan - the flat interest grows with tenure, so a longer tenure makes P worse, not better.
- Re-arranging the fee as a deduction at a later date - the cash cost is unchanged, only its timing.
The useful rule: a flat rate on a two-year loan is roughly 1.8 times the equivalent reducing-balance rate, so a flat quote must be compared with a reducing quote only after conversion. Here, flat 9% is far more expensive than reducing 12%.