Two Loan Offers and a Sinking Fund: Choosing a Lender for a Power Loom
A women's self-help group in Jorhat has been quoted ₹1,80,000 for a power loom and must choose between two lenders. Nadia Cooperative Bank offers the full amount at 12% per annum compounded quarterly for 36 months, with principal and interest repayable as a single lump sum at maturity and no processing fee. Barsapara Gramin Bank offers 11.5% per annum compounded monthly for the same 36 months, but deducts a one-time processing fee of ₹3,600 from the sanctioned amount, so the group would actually receive only ₹1,76,400 while interest is still charged on ₹1,80,000. The treasurer argues that the second offer must be cheaper because 11.5% is a lower rate than 12%. The group also plans to deposit an equal amount at the end of every month into a recurring deposit paying 9% per annum compounded monthly, timed to mature exactly when the loan falls due. Before signing, the members want the true cost of each loan, the monthly deposit needed, and a defensible choice.
1. Compute the lump sum each lender will claim at the end of 36 months, convert both to effective annual rates, and say whether the treasurer's reasoning holds.
Read the worked answer
Nadia Cooperative Bank. 12% p.a. compounded quarterly gives i = 0.12/4 = 0.03 per quarter and n = 3 × 4 = 12 quarters. A = 1,80,000(1.03)^12 = 1,80,000 × 1.425761 = ₹2,56,637.
Barsapara Gramin Bank. i = 0.115/12 = 0.0095833 per month, n = 36. A = 1,80,000(1.0095833)^36 = 1,80,000 × 1.409673 = ₹2,53,741.
Effective annual rates. Nadia: (1.03)^4 − 1 = 12.55%. Barsapara: (1.0095833)^12 − 1 = 12.13%. Compounding frequency is part of the price, so the 12% loan is dearer despite the higher nominal figure.
The treasurer reached the correct lender for the wrong reason. He compared nominal rates, which are not comparable when the compounding periods differ. Also note the size of the gap: only ₹2,896 on a ₹1.8 lakh loan, about 1.1%. A decision resting on such a thin margin should be checked against fees and cash-flow timing, not just the rate.
2. How much must the group set aside at the end of each month to repay the loan from the recurring deposit at 9% p.a. compounded monthly? Give the figure for each lender.
Read the worked answer
This is the future value of an ordinary annuity: R[((1+i)^n − 1)/i] = A, with i = 0.09/12 = 0.0075 and n = 36.
(1.0075)^36 = 1.308648, so the annuity factor is (1.308648 − 1)/0.0075 = 0.308648/0.0075 = 41.153.
Against Nadia's ₹2,56,637: R = 2,56,637/41.153 = ₹6,237 per month. Against Barsapara's ₹2,53,741: R = 2,53,741/41.153 = ₹6,166 per month.
The difference in monthly saving is only about ₹71, which reinforces how narrow the price gap is. The real risk is behavioural: a recurring deposit must be funded every month for three years, and a missed instalment during a lean weaving month costs a penalty and breaks the schedule. The lumpsum repayment date is fixed, so the deposit schedule is not optional.
3. Given that the ₹3,600 fee may be deducted from the loan or paid separately from the group's own savings, recommend a lender and state what non-price factors could reverse your answer.
Read the worked answer
Fee deducted (the stated offer). The group receives ₹1,76,400 and repays ₹2,53,741, a cost of 43.84% of receipts. Nadia gives ₹1,80,000 for ₹2,56,637, a cost of 42.58%. Nadia wins.
Fee paid from savings. Total outflow under Barsapara becomes 2,53,741 + 3,600 = ₹2,57,341 against ₹2,56,637 for Nadia. Nadia still wins, but by only ₹704 - well inside the error of any estimate.
Recommendation: sign with Nadia, where the loan is cheapest on both readings and no upfront cash is needed.
What could reverse it: (i) if the group has no savings to pay the fee, the deducted-fee calculation applies and the gap widens in Nadia's favour - so this does not help Barsapara; (ii) a prepayment clause, since the group may want to clear the loan early after a good season; (iii) the recurring deposit minimum and penalty structure at each bank; (iv) if Barsapara will reduce the fee to below ₹700, the two offers are effectively identical and service quality decides. The group should ask both banks in writing about foreclosure charges before signing.