Compound growth and projections in EPSO numerical reasoning
A value grows or falls by a fixed rate for several years, months or days, and you need the end value. Each period applies to the result of the previous one, which is why adding the rates up gives a wrong answer that sits very close to the right one.
8,573 answers, last 60 days · The test gives you 2 minutes per question (10 questions in 20 minutes).
How to recognise it
- If X grows by 3% a year, what will it be in 2027?
- If the price increases each day by 0.75%, how much will it be on 13 July?
- Assuming the same annual rate continues, what will X be in two years?
The method
- Count the periods exactly: from 8 July to 13 July there are 5 daily increases, not 6.
- Turn the rate into a factor: +3% gives 1.03, −4% gives 0.96.
- Multiply the starting value by the factor once per period.
- If two periods have different rates, multiply by each factor in turn.
Worked example
A question from our bank, in EPSO format.
| Metal | 4 July | 5 July | 6 July | 7 July | 8 July |
|---|---|---|---|---|---|
| Platinum | 720,421 | 698,645 | 702,345 | 809,623 | 956,879 |
| Palladium | 321,592 | 301,234 | 410,568 | 451,879 | 543,901 |
| Gold | 36,421 | 36,432 | 36,440 | 36,554 | 36,600 |
| Silver | 816,220 | 828,431 | 824,522 | 833,150 | 809,776 |
Unit: € per kg
If from 8 July the trading price of gold increases each day by 0.75%, how much will it be on 13 July?
Choose an answer to see the solution.
The traps
Simple growth instead of compound growth
Adding the rates (5 × 0.75% = 3.75%) ignores that each increase applies to an already increased value. In the example the two answers are €20 apart: estimation will not separate them, the calculation must.
Miscounting the periods
From 2021 to 2024 there are three annual changes; from 8 to 13 July, five daily ones. In the example, three of the four wrong options are the right method with the wrong number of periods.
Average annual rate is not total growth divided by years
A value that doubles in four years grows by about 18.9% a year, not 25%. To find the annual rate, test the options: multiply the start by (1 + option) as many times as there are years and see which lands on the end value.
With the EPSO calculator
No power key is needed. Type the starting value, then × 1.0075 five times, ticking each period on the notepad. For a fall, the factor is below 1 (−4% is × 0.96).
Practise this calculation
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Frequently asked questions
How do I calculate compound growth on the EPSO basic calculator?
Multiply by the factor (1 + rate) once per period: for 5 periods at 0.75%, multiply by 1.0075 five times. Count the periods on the notepad.
Why is simple growth wrong in EPSO projection questions?
Each period applies to the value reached after the previous period, so the increases compound. Adding the rates gives a slightly lower figure, which EPSO places among the options.