Comparing a Moneylender Loan and a Savings Group Loan
A market seller in Kakata needs L$45,000 to restock her stall before a festival. A moneylender offers the amount at 12% simple interest per annum, repayable after 8 months in one payment. A savings group offers the same amount at a flat '3% per month on the original amount,' repayable in 8 monthly instalments of equal principal plus interest. The seller expects to earn L$58,000 in sales over the eight months, but only if she keeps at least L$6,000 for transport and stall fees. She has saved L$4,000. A friend says the savings group is cheaper because '3% is less than 12%.' The savings group meets weekly and requires a witness for each payment; the moneylender requires no collateral but knows her stall.
1. Calculate total repayment under each offer and verify or refute the friend's claim. Show formulas.
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Moneylender: I = P r t = 45,000 × 0.12 × 8/12 = 3,600. Total = 48,600. Savings group: flat interest = 45,000 × 0.03 × 8 = 10,800. Total = 55,800. The friend is wrong. 3% per month is not being compared with 12% per year on the same basis; over eight months the flat charge is 24% of the principal, while the moneylender charges 8% for the same period (12% × 8/12). The savings group costs 7,200 more. The equal principal instalment is 45,000/8 = 5,625, and monthly interest is 1,350, so each payment is 6,975. The friend compared a monthly rate with an annual rate without converting.
2. The seller says she prefers the savings group because the payments are smaller than repaying L$48,600 at once. Evaluate this reasoning using the monthly payment amount and her L$4,000 savings. Recommend one option and state one condition under which your recommendation would change.
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The monthly payment is indeed smaller: 6,975 versus a 48,600 lump sum. But smaller instalments do not make the loan cheaper; total repayment is 7,200 higher. The cash-flow test is whether she can meet 6,975 each month while keeping 6,000 for transport and stall fees. Expected sales are 58,000 over eight months, and her savings are 4,000, so total available is 62,000. The savings-group route costs 55,800 plus 6,000 = 61,800, leaving only 200 as a buffer. That is very tight. The moneylender route costs 48,600 + 6,000 = 54,600, leaving 7,400, but requires her to hold funds until the end. I would recommend the moneylender if she can keep the money separately and repay on time. The recommendation would change if her sales arrive late or she cannot resist spending the lump sum; then the disciplined monthly schedule may be worth the extra 7,200, or she should borrow less.
3. Suppose the savings group instead charged 3% per month on the reducing balance. Without calculating a full schedule, explain whether this would make the savings group cheaper or more expensive than the moneylender, and why.
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It would be cheaper than the flat-rate savings group but still more expensive than the moneylender. On a reducing balance, interest is charged each month on the amount still owed. The balance falls from 45,000 toward 5,625, so the average balance is roughly half the original. A 3% monthly charge on that average is about 1.5% of 45,000 per month, or roughly 12% of the original over eight months, which is close to 5,400–6,100 in interest. That is far below 10,800 but still above the moneylender's 3,600. The exact total would require a schedule, but the comparison is clear: the moneylender's 12% annual simple interest over 8/12 of a year is 8% of principal, while 3% monthly on a declining balance over eight months is still a much higher annualized rate.