'Interest-Free' in Shymkent: Two Credit Offers for One Refrigerator
The Sarsenov family in Shymkent has chosen a refrigerator that costs exactly 320,000 tenge in every store. Their net monthly income is 180,000 tenge, of which 60,000 is already committed to a car loan and utilities. They have 90,000 tenge in savings and have agreed that 40,000 tenge must stay untouched as an emergency reserve.
Store A offers credit with a mandatory 20% down payment, a nominal annual rate of 24% (2% per month, equal annuity payments), a term of 12 months, and a one-off commission of 2% of the financed amount, paid on the day of purchase.
Store B offers '0% interest' for 12 months with no down payment, but charges a monthly account fee of 6,500 tenge and a one-off insurance premium of 2% of the price, paid upfront.
A salesperson at Store B tells them: 'Ours is interest-free, so it is obviously the cheaper way to buy.'
1. Calculate the monthly payment and the total amount the family would pay (upfront costs plus all monthly payments) under each store's offer.
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Store A. The down payment is 20% of 320,000 = 64,000 tenge, so the financed amount is 256,000 tenge. The monthly rate is 2% = 0.02 and n = 12.
Annuity payment = P·i / (1 − (1+i)^−n). Here (1.02)^12 = 1.2682, so 1/1.2682 = 0.7885 and the denominator is 1 − 0.7885 = 0.2115.
Payment = (256,000 × 0.02) / 0.2115 = 5,120 / 0.2115 ≈ 24,200 tenge per month.
Twelve payments = 24,200 × 12 ≈ 290,400 tenge. The commission is 2% of 256,000 = 5,120 tenge, paid with the down payment.
Total A ≈ 64,000 + 290,400 + 5,120 ≈ 359,500 tenge, of which 69,120 tenge is due on day one.
Store B. The price is split over 12 months: 320,000 / 12 ≈ 26,667 tenge, plus the fee 6,500 = 33,167 tenge per month. Total monthly outlay = 33,167 × 12 = 398,000 tenge. Insurance is 2% of 320,000 = 6,400 tenge upfront.
Total B = 398,000 + 6,400 = 404,400 tenge, of which only 6,400 tenge is due on day one.
Note that the two offers differ in the timing of cash outflows, not only in the sum: A demands a large payment now, B demands more every month.
2. Using the family's emergency-reserve rule, determine which offer they can actually sign today. If they can save 15,000 tenge per month, how long must they wait before the cheaper total option becomes available, and is waiting the better decision?
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What cash is really available. Savings 90,000 − reserve 40,000 = 50,000 tenge of usable cash.
Test A: it requires 69,120 tenge on day one. 69,120 > 50,000, short by 19,120 tenge - the family cannot take A today without breaking their own reserve rule.
Test B: it requires 6,400 tenge on day one, which fits inside 50,000. B is feasible today.
Cheapest executable plan today = B, at 404,400 tenge total (monthly burden 33,167 tenge, which is 27.6% of the 120,000 tenge of free monthly income - heavy but survivable).
Waiting. The shortfall for A is 19,120 tenge. At 15,000 tenge per month, one month gives 15,000 (still short by 4,120), two months gives 30,000 - enough. So A becomes possible after 2 months.
Is waiting worth it? The saving is 404,400 − 359,500 = 44,900 tenge. The cost of waiting is two months without a refrigerator. If the old appliance still works, waiting two months and then taking A is clearly rational: roughly 45,000 tenge - about a quarter of the purchase price - is bought with a delay, not with money. If the refrigerator has already failed and food is being spoiled weekly, that calculation can reverse.
A third route worth naming: buy nothing on credit, save the 15,000 plus the 33,167 they would have paid monthly, and pay cash later - but the arithmetic shows this takes far longer than two months.
3. Evaluate the salesperson's claim that Store B is cheaper because it charges no interest. Support your answer with figures.
Read the worked answer
The claim confuses a label with a cost. 'Zero percent' applies to the nominal interest rate only; the price of borrowing is whatever the customer pays above the cash price.
- Store B extra charges: 404,400 − 320,000 = 84,400 tenge, i.e. 26.4% of the price over 12 months.
- Store A extra charges: 359,500 − 320,000 = 39,500 tenge, i.e. 12.3% of the price over 12 months.
So the 'interest-free' loan costs more than twice as much in financing charges as the loan with a visible 24% nominal rate. The reason is that A amortises a shrinking balance, while B charges a flat fee on the full price every month for the whole year.
The honest comparison is not the advertised rate but (i) the total paid, and (ii) the upfront cash demanded. B wins only on the second measure - 6,400 versus 69,120 tenge. The salesperson's statement is therefore true only in a narrow, misleading sense: B is the more accessible offer, not the cheaper one.