Reducing-Balance Lending versus Flat Rate
Tara Microfinance Bank's Nsukka branch is assessing a ₦2,400,000 loan application from a market traders' association that wants to buy a cold room. The bank lends at 2% per month on the reducing balance, repayable in 12 equal monthly instalments, the first falling due one month after drawdown.
The credit officer has instead computed the charge on a flat basis - ₦48,000 a month for 12 months - and told the client her total interest will be ₦576,000. The client says she cannot pay more than ₦200,000 a month. Branch policy caps lending at four times verified monthly contribution, which for this association is ₦520,000.
A rival cooperative has advertised '12% per annum flat', and the client is convinced it is far cheaper than Tara's 2% a month. The credit officer wants to match the rival's headline figure to win the business.
Relevant annuity factor: 12 periods at 2% = 8.9826.
1. Compute the correct monthly instalment and total interest on the ₦2,400,000 loan, and explain why the credit officer's ₦576,000 is wrong.
Read the worked answer
Instalment EMI = P × i ÷ [1 − (1 + i)^−n] (1.02)^12 = 1.218994, so (1.02)^−12 = 0.820348 and the denominator = 0.179652. EMI = (2,400,000 × 0.02) ÷ 0.179652 = 48,000 ÷ 0.179652 = ₦267,184 (approximately). Total repayments = ₦267,184 × 12 = ₦3,206,208 Total interest = ₦806,208
Why the flat figure is wrong Flat interest charges 2% on the full ₦2,400,000 every month even though the balance falls as instalments are paid. Reducing balance charges interest only on the outstanding balance. The flat method understates the true cost by about ₦230,000 and, more importantly, understates the monthly cash burden: the flat calculation implies an instalment of (2,400,000 + 576,000) ÷ 12 = ₦248,000, against the true ₦267,184, a shortfall of about ₦19,000 a month.
Implication Quoting the flat figure is not a harmless simplification - it misleads the borrower about affordability and is inconsistent with honesty and fair treatment of customers. The correct instalment and total cost should be given in writing before the facility letter is signed, and the credit officer should be corrected and retrained rather than allowed to quote flat rates to match competitors.
2. What is the largest loan the client can service at ₦200,000 a month over 12 months? Reconcile that with the branch cap and recommend a structure.
Read the worked answer
Affordability limit (12 months) Maximum principal = EMI × annuity factor = ₦200,000 × 8.9826 = ₦1,796,520.
Policy ceiling 4 × ₦520,000 = ₦2,080,000.
Reconciliation Affordability binds: ₦1,796,520 is about ₦283,480 below the policy ceiling. The cap is a maximum, never a target; a loan of ₦2,080,000 over 12 months would require an instalment of 2,080,000 ÷ 8.9826 = ₦231,560, which she cannot service.
Alternative structure If the association genuinely needs the full ₦2,080,000, lengthen the tenor. Required factor = 2,080,000 ÷ 200,000 = 10.4. a(13, 2%) = 9.7903 and a(14, 2%) = 10.5787, so 14 months is needed. EMI over 14 months = 2,080,000 ÷ 10.5787 = ₦196,620, within the ₦200,000 budget. Total interest rises to (14 × 196,620) − 2,080,000 = ₦672,680, against ₦672,672 on the lower principal over 12 months - she borrows more and pays about the same monthly, at the price of a longer exposure.
Recommendation Offer ₦1,796,500 over 12 months, or ₦2,080,000 over 14 months if the cold room's projected cash flows support it. Verify the ₦520,000 contribution figure independently, take security or a group guarantee, and note that extending the tenor increases credit risk even though the monthly payment looks safer.
3. The client believes the cooperative's '12% per annum flat' is far cheaper than Tara's 2% a month. Demonstrate the comparison and advise what the bank should do.
Read the worked answer
Convert the rival's quote to a comparable basis Flat 12% p.a. on ₦2,400,000 for 12 months: interest = ₦288,000; total ₦2,688,000; monthly instalment = ₦224,000.
Find the reducing-balance monthly rate producing that instalment: Annuity factor required = 2,400,000 ÷ 224,000 = 10.7143 a(12, 1.75%) = 10.7405; a(12, 1.80%) = 10.7118 Interpolating, i ≈ 1.80% per month, i.e. about 21.6% a year nominal and 1.018^12 − 1 = 23.9% effective.
Quick check using the standard approximation: flat rate × 2n ÷ (n + 1) = 12% × 24/13 ≈ 22.2% reducing balance - consistent with the interpolation.
Comparison Tara at 2% a month is 24% nominal and 26.8% effective. The cooperative is therefore genuinely slightly cheaper, but the client's belief that '12%' is half of '24%' is an apples-to-oranges reading: a flat rate of 12% is roughly equivalent to 22% on a reducing balance.
What the bank should do Quote the true instalment (₦267,184) and the effective annual cost in writing, and explain the flat-versus-reducing distinction so the borrower can compare properly. The bank must not advertise a flat rate to match the competitor's headline: knowingly quoting a basis that understates the cost would breach integrity, professional behaviour and fair treatment of customers, and exposes the bank to consumer-protection complaints. Compete on speed, service and transparency instead.