Total the installment plan first.
total = down + monthly × months
every peso that leaves your pocket
= 3,000 + 1,400 × 12
multiplication before addition
= ₱19,800
the real price of the phone
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Installment Buying: The Real Price
Down payment plus every monthly payment — that is what you really pay. The gap between that and the cash price is the cost of paying slowly.
The problem
A phone's cash price is ₱18,000. On installment it is ₱3,000 down and ₱1,400 a month for 12 months. How much MORE than the cash price is the installment plan?
Total paid = 3,000 + 1,400 × 12 = 3,000 + 16,800 = ₱19,800; against the cash price, 19,800 − 18,000 = ₱1,800 extra. B stops at the total without subtracting — it answers "how much in all", a different question. C forgets the down payment: 1,400 × 12 = 16,800 against 18,000 is a ₱1,200 gap — and it runs the wrong way, making the installment look cheaper than cash.
The finance charge is the difference.
finance charge = total − cash price
what paying slowly costs
= 19,800 − 18,000 = ₱1,800
the extra on top of cash
Turn it into a percent — of the cash price.
1,80018,000 = 10%
the surcharge as a rate
The base is the cash price, not the installment total: the question "how much more than cash" measures against cash. Dividing by 19,800 gives 9.1% — a plausible-looking wrong answer exams are happy to print.
When the charge is added to the balance: find the monthly payment.
A ₱24,000 appliance: 25% down, a 12% finance charge added to the balance, and the result paid in 12 equal monthly payments. How much is each payment?
down = 0.25 × 24,000 = 6,000
paid at once
balance = 24,000 − 6,000 = 18,000
only this is financed
18,000 × 1.12 = 20,160
the charge is on the BALANCE
20,160 ÷ 12 = ₱1,680 a month
the down payment is not divided
If the charge is instead “1.5% of the balance per month” for those 12 months, it is 18,000 × 0.015 × 12 = ₱3,240 in all, so each payment is (18,000 + 3,240) ÷ 12 = ₱1,770. Charging the 1.5% only once is the usual slip.
Not 12% of the cash price
24,000 × 1.12 = 26,880 charges interest on money already paid as the down payment. Subtract the down payment first, then add the charge.
Backwards: “the total is 16% more than the cash price”.
₱8,000 down and ₱2,500 a month for 20 months. This total is 16% more than the cash price. Find the cash price.
total = 8,000 + 2,500 × 20 = 58,000
step 1 as usual
1.16 × cash = 58,000
16% more than cash means × 1.16
cash = 58,000 ÷ 1.16 = ₱50,000
divide; do not take 16% off
58,000 × 0.84 = ₱48,720 is the trap: the 16% was measured on the cash price, not on the total. Check: 50,000 × 1.16 = 58,000 ✓.
Variations: the number of months unknown, the charge as a yearly rate.
How many payments? A ₱27,000 aircon is bought with ₱5,000 down and ₱1,250 a month. The finance charge comes to ₱3,000. How many monthly payments are there?
total = 27,000 + 3,000 = 30,000
cash price + finance charge
left after the down payment: 30,000 − 5,000 = 25,000
what the monthly payments cover
25,000 ÷ 1,250 = 20 months
check: 5,000 + 1,250 × 20 = 30,000 ✓
What is different: the months are the unknown. Dividing 27,000 by 1,250 (21.6) forgets both the charge and the down payment.
The charge as a yearly rate. A ₱15,000 balance carries a ₱1,800 finance charge and is paid off in 6 months. What simple yearly rate is that?
R = I ÷ (PT)
simple interest, run backwards
= 1,800 ÷ (15,000 × 612)
6 months is half a year
= 1,800 ÷ 7,500 = 0.24 = 24% a year
12% for half a year
What is different: “as a percent of the balance” and “as a yearly rate” are different questions. Over 6 months, a 12% charge is a 24% yearly rate.
Not 12%
1,800 ÷ 15,000 = 12% is the charge for the whole 6 months. A yearly rate has to account for the time, so divide by the half year as well.
The three slips that lose these marks.
| Slip | What it looks like |
|---|---|
| down payment dropped | 1,400 × 12 = 16,800 "total" |
| stopping at the total | answering 19,800 to a "how much more" question |
| wrong percent base | dividing the charge by the installment total |
| charge on the cash price | adding the finance charge before taking off the down payment |
On the exam
Expect the finance charge (total minus cash), the monthly payment when a charge is added to the balance, the charge as a percent of cash, or the cash price worked back from “x% more”. Lay out down payment, balance, charge and payments in that order. Check: down payment + all monthly payments must equal the total you used.
Check: rebuild the total from the answer.
cash + charge
18,000 + 1,800 = 19,800
matches down + 12 months ✓
sanity
installment > cash
paying slowly always costs more ✓
Now you try
Practice problem
The problem
A laptop's cash price is ₱10,400. On installment: ₱2,000 down and ₱900 a month for 10 months. What is the finance charge?
Total = 2,000 + 900 × 10 = ₱11,000; finance charge = 11,000 − 10,400 = ₱600. D is the total, not the charge. B compares the monthly payments alone: 900 × 10 = 9,000 against 10,400 is a ₱1,400 gap, but it leaves out the ₱2,000 down payment, which is part of what you pay.