To compare instalment plans, find the total paid under each one and compare the extra over the cash amount. The smallest monthly payment comes from spreading the cost over more months, so it does not show the smallest total.
This lesson is part of rates and percentages in multistep consumer questions. Every plan here is invented, and real offers change.
What are the steps?
Use the same working for each plan.
- Total paid = monthly payment × number of months, plus any fee.
- Extra paid = total paid − cash amount.
- Extra as a percentage = extra ÷ cash amount × 100.
Worked example: three invented plans
A laptop is sold for RM3 600 in cash. Three plans are supplied.
Plan A. 12 payments of RM320, with an RM60 processing fee. Total = 12 × 320 + 60 = RM3 900.
Plan B. 24 payments of RM175 and no fee. Total = 24 × 175 = RM4 200.
Plan C. Flat rate of 4% a year for 3 years on RM3 600. Interest = 3 600 × 0.04 × 3 = RM432.
Total = 3 600 + 432 = RM4 032. Monthly payment = 4 032 ÷ 36 = RM112.
| Plan | Monthly payment | Total paid | Extra over cash | Extra as % of cash |
|---|---|---|---|---|
| A | RM320 | RM3 900 | RM300 | 8.3% |
| B | RM175 | RM4 200 | RM600 | 16.7% |
| C | RM112 | RM4 032 | RM432 | 12% |
Plan C has the smallest monthly payment, but Plan A has the smallest total. Plan A pays RM132 less than Plan C overall.
The mistake of choosing the smallest monthly payment
A common slip is to choose Plan C because RM112 is the lowest figure each month. The plan runs for 36 months, so the extra adds up.
Always multiply by the number of months first. Then decide with the total and with the extra paid.
Check yourself
The cash amount is RM2 400. Plan X is 10 payments of RM250 with an RM30 processing fee. Plan Y is 18 payments of RM145.
Plan Z is a flat rate of 5% a year for 2 years. Which plan has the smallest total?
Answer
Plan X: 10 × 250 + 30 = RM2 530, which is RM130 over cash.
Plan Y: 18 × 145 = RM2 610, which is RM210 over cash.
Plan Z: interest = 2 400 × 0.05 × 2 = 240, so total = RM2 640, which is RM240 over cash. Monthly payment = 2 640 ÷ 24 = RM110.
Plan X has the smallest total, and Plan Z has the smallest monthly payment.
What to study next
Finish the series with explaining why a larger discount percentage can still give a higher amount to pay. Then try the integrated practice set.
If you want a teacher to go through your plan comparisons, see online one-to-one Mathematics tuition.