Choosing Between Two Small-Ticket Loan Quotes
A branch customer needs ₹60,000 for 24 months. The bank offers two quotes. Quote X charges simple interest at 11% per annum and a one-time processing fee of 1.25% of the loan amount. Quote Y charges compound interest at 10% per annum compounded annually and a one-time processing fee of 0.80% of the loan amount. In both cases the principal is repaid with interest at the end of 24 months; no intermediate payments are made. The customer has a monthly surplus of ₹2,700 and says he can repay a lump sum only from a bonus expected after 24 months. The branch officer must compare the total repayment, not just the stated interest rate, and then check whether the customer would need to set aside more than ₹2,500 per month to meet the better quote. Ignore taxes and other charges. All amounts are in rupees.
1. Calculate total repayment under Quote X and Quote Y. Which quote costs less, and by how much?
Read the worked answer
Quote X:
- Simple interest = 60,000 × 11/100 × 2 = ₹13,200.
- Processing fee = 1.25% of 60,000 = ₹750.
- Total repayment = 60,000 + 13,200 + 750 = ₹73,950.
Quote Y:
- Amount after 2 years = 60,000 × (1.10)^2 = 60,000 × 1.21 = ₹72,600.
- Interest component = 72,600 − 60,000 = ₹12,600.
- Processing fee = 0.80% of 60,000 = ₹480.
- Total repayment = 60,000 + 12,600 + 480 = ₹73,080.
Quote Y costs less by ₹73,950 − ₹73,080 = ₹870.
2. What monthly amount must the customer set aside to meet the cheaper quote over 24 months? Compare this with his ₹2,700 surplus.
Read the worked answer
The cheaper quote is Quote Y with total repayment ₹73,080.
Monthly set-aside required = ₹73,080 ÷ 24 = ₹3,045.
The customer’s monthly surplus is ₹2,700. So he is short by ₹3,045 − ₹2,700 = ₹345 per month. Over 24 months the total shortfall is ₹345 × 24 = ₹8,280. He would need a bonus of at least ₹8,280, or he must reduce other commitments, to meet Quote Y without defaulting. The required monthly set-aside is also above ₹2,500, so the answer to the officer’s check is yes: more than ₹2,500 per month is needed.
3. The customer argues that compounding always makes a loan costlier, so Quote Y cannot be cheaper. Evaluate this claim using the numbers.
Read the worked answer
The claim is not valid here. Compounding does increase the interest effect within Quote Y, but the comparison must use the total cash outflow, including the rate and the fee. Quote X has a higher nominal rate (11% simple) and a higher fee (1.25%), giving total repayment ₹73,950. Quote Y has a lower nominal rate (10% compounded annually) and a lower fee (0.80%), giving total repayment ₹73,080. The extra compounding in Y does not outweigh the lower rate and lower fee. As a percentage of principal, total cost is 23.25% for X and 21.8% for Y. So Quote Y is cheaper, but the officer should still check repayment capacity because the monthly set-aside needed is ₹3,045, above the customer’s surplus.