To compare saving plans, calculate the final amount for each plan under the same assumptions. The higher rate does not always win, because the period and the way interest is added both matter.
This lesson is part of the consumer mathematics and financial planning section. It follows building a cash-flow statement from supplied data.
Which assumptions must match?
Write these down before you calculate, and check that every plan uses the same ones.
- The amount saved at the start.
- The length of time.
- Whether interest is simple or compounded, and how often.
- The rate stays fixed and nothing is withdrawn.
Worked example: three invented plans
Aina saves RM5 000 for 3 years under each plan.
Plan A: 4% simple interest. Interest = 5 000 × 0.04 × 3 = RM600. Total = RM5 600.
Plan B: 3.8% compounded yearly. Total = 5 000 × 1.038³ = RM5 591.93.
Plan C: 4% compounded yearly. Total = 5 000 × 1.04³ = RM5 624.32.
After 3 years, Plan C is largest, Plan A is next, and Plan B is smallest. Plan A is RM8.07 ahead of Plan B because its rate is 0.2 percentage points higher.
Now extend Plans A and B to 10 years. Plan A gives 5 000 + 5 000 × 0.04 × 10 = RM7 000. Plan B gives 5 000 × 1.038¹⁰ = RM7 260.12.
Over 10 years, Plan B is larger, because compounding has more time to work. The period changes the ranking.
The mistake of comparing rates only
A common slip is to choose the plan with the highest rate and stop. Plan A’s 4% looks higher than Plan B’s 3.8%, yet compounding lets Plan B overtake it over 10 years.
The remedy is to calculate each final amount. A rate is an input, and the final amount is the answer.
Check yourself
Compare RM2 000 saved for 4 years at 5% simple interest with the same amount at 4.5% compounded yearly. Which is larger?
Answer
Simple: interest = 2 000 × 0.05 × 4 = 400, so total = RM2 400.
Compound: 2 000 × 1.045⁴ = RM2 385.04.
The simple plan is larger by RM14.96 over 4 years. Over a longer period, the compounding plan could overtake it, so state the period when you compare.
What to study next
Judge whether a plan reaches a goal in checking whether a financial plan meets a numerical goal. You can explore percentage bases in the percentage base and index explorer.
If you want a teacher to go through your comparisons, see online one-to-one Mathematics tuition.