Two Loan Offers for an SHG
A self-help group needs ₹80,000 for two years to buy a food-processing machine. It receives two offers. Bank A charges 12% per annum simple interest and a processing fee of 1% of the loan amount, deducted upfront. Bank B charges 10% per annum compounded annually and a processing fee of ₹1,200, also deducted upfront. The group will repay the principal and interest at the end of two years. The group chairperson says, 'A 10% compounded loan must be cheaper than a 12% simple-interest loan because 10 is less than 12.' A member points out that the processing fees and the compounding method must be compared, not just the headline rates. You are asked to calculate the total cash outgo under each offer, recommend one, and test the chairperson's statement. Ignore taxes and other charges.
1. Calculate the total cash outgo under both offers and recommend one.
Read the worked answer
Bank A - simple interest Interest = 80,000 × 12/100 × 2 = ₹19,200. Processing fee = 1% of 80,000 = ₹800. Total cash outgo = 80,000 + 19,200 + 800 = ₹1,00,000.
Bank B - compound interest Amount = 80,000 × (1.10)^2 = 80,000 × 1.21 = ₹96,800. Interest = 96,800 − 80,000 = ₹16,800. Processing fee = ₹1,200. Total cash outgo = 80,000 + 16,800 + 1,200 = ₹98,000.
Bank B is cheaper by ₹2,000 on total cash outgo. Recommendation: choose Bank B if there are no other conditions such as prepayment penalties, collateral, or delayed disbursement.
2. Evaluate the chairperson's reasoning and state when, ignoring fees, the 10% compounded offer would become costlier than the 12% simple offer.
Read the worked answer
The chairperson is comparing only the headline rates, not the total cost. For two years, 10% compound interest gives a factor of 1.21, i.e. 21% of principal, while 12% simple interest gives 24% of principal. So at two years the 10% compounded offer is cheaper on interest.
Compounding catches up as the tenor lengthens:
- 4 years: 1.10^4 = 1.4641 vs 1 + 0.12 × 4 = 1.48 - still cheaper.
- 5 years: 1.10^5 = 1.61051 vs 1 + 0.12 × 5 = 1.60 - now costlier by about 0.01051 × 80,000 = ₹840.80 before fees.
So the statement is not generally true; it depends on the tenor, and fees can shift the crossover.
3. What upfront fee on Bank B would make the total cash outgo equal? What does this show about comparing loans?
Read the worked answer
Bank A total = ₹1,00,000. Bank B principal + interest = ₹96,800. For equality, Bank B fee = 1,00,000 − 96,800 = ₹3,200. The current fee is ₹1,200, so it would have to rise by ₹2,000 to erase Bank B's advantage.
This shows that a lower headline interest rate is not enough. A borrower must compare total cash outgo, including fees, the compounding method, the tenor, and the timing of disbursement and repayment. A fee difference of ₹2,000 is enough to reverse a seemingly clear rate advantage in this case.