Three Loan Offers and One Headline Rate
Ramesh Patil, a dairy farmer in Satara, needs ₹5,00,000 for 24 months to buy a bulk milk chiller. Three offers are on the table. Offer A: flat rate 10.50% per annum, repayable in 24 equal monthly instalments, foreclosure allowed after 12 instalments with no rebate on interest already charged. Offer B: 11.50% per annum on reducing balance, 24 equal monthly instalments, foreclosure at any time on payment of outstanding principal plus accrued interest, no charge. Offer C: flat 9.75% per annum with a 2% processing fee deducted from the disbursement, 24 equal monthly instalments. The branch manager tells him to 'just compare the rates and pick the lowest'. Ramesh can spare about ₹26,000 a month and may need to foreclose after 12 months if the chiller purchase is deferred. He asks the LBO to explain, in rupee terms, which offer actually costs him least.
1. Compute the monthly instalment and total interest under each offer, and rank the three by total cash the customer parts with.
Read the worked answer
Offer A (flat 10.50%): interest = 5,00,000 × 10.50% × 2 = ₹1,05,000. Total = ₹6,05,000. Instalment = 6,05,000 / 24 = ₹25,208. Total interest ₹1,05,000.
Offer B (11.50% reducing): EMI = P·r·(1+r)^n / ((1+r)^n − 1), with r = 0.115/12 = 0.0095833 and n = 24. (1+r)^24 = 1.2572, so EMI = 5,00,000 × 0.0095833 × 1.2572 / 0.2572 ≈ ₹23,420. Total outgo = 23,420 × 24 = ₹5,62,080; total interest ≈ ₹62,080.
Offer C (flat 9.75% + 2% fee): interest = 5,00,000 × 9.75% × 2 = ₹97,500. Total = ₹5,97,500; EMI = ₹24,896. The 2% fee of ₹10,000 is deducted upfront, so he actually receives ₹4,90,000 and pays back ₹5,97,500 - an economic outgo of ₹6,07,500.
Ranking by cash out: B (₹5,62,080) < A (₹6,05,000) < C (₹6,07,500). The offer with the lowest quoted rate is the most expensive one; the manager's advice is wrong.
2. Convert each offer into an effective annual cost so the comparison is like-for-like, and explain to Ramesh why the flat rate misleads.
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Why flat misleads: a flat rate charges interest on the full ₹5,00,000 for the whole 24 months even though the principal is shrinking every month. Reducing balance charges interest only on the balance actually outstanding. So 10.50% flat is not comparable with 11.50% reducing.
Effective cost by the internal-rate-of-return route (find the monthly rate at which the present value of the instalments equals the money actually received):
- A: 5,00,000 / 25,208 = annuity factor 19.83 for 24 months - about 1.58% per month, i.e. roughly 19% nominal, ~20.8% effective annual.
- B: quoted reducing rate is already an IRR - ~12.1% effective annual ((1.0095833)^12 − 1).
- C: 4,90,000 / 24,896 = factor 19.68 - about 1.65% per month, i.e. ~19.8% nominal, ~21.7% effective annual.
What to tell the customer: ask every lender for the reducing-balance rate and the APR, plus all fees, and compare those three numbers only. On that basis B is the cheapest by a wide margin (roughly 12% versus 21%), and C - the one that looks cheapest at 9.75% - is the costliest because the fee is charged on money he never gets to use.
3. Ramesh may foreclose after 12 instalments. Does the ranking change? Show the arithmetic.
Read the worked answer
Offer A after 12 EMIs: paid 12 × 25,208 = ₹3,02,500, of which ₹52,500 was interest. On a flat schedule the principal is usually recovered evenly, leaving ₹2,50,000 outstanding. Total cost of funds = 3,02,500 + 2,50,000 = ₹5,52,500.
Offer B after 12 EMIs: balance = P(1+r)^12 − EMI × [((1+r)^12 − 1)/r]. With (1+r)^12 = 1.12126 and the annuity factor 12.65: 5,00,000 × 1.12126 = ₹5,60,630, less 23,420 × 12.65 = ₹2,96,260, leaving ≈ ₹2,64,370. Total cost = 2,81,040 + 2,64,370 = ₹5,45,410.
Offer C after 12 EMIs: 12 × 24,896 = ₹2,98,750 plus ₹2,50,000 principal plus the ₹10,000 fee already paid = ₹5,58,750.
Conclusion: B still wins, but the margin over A collapses from about ₹43,000 to about ₹7,000, because A front-loads its interest and gives nothing back on early closure. Two practical cautions: confirm in writing whether A levies a foreclosure charge (a 2% charge, about ₹5,000, would erase the gap and make A cheaper), and check whether A refunds unearned interest. If foreclosure is likely, the reducing-balance offer is the safer choice even on a small margin.