Topic 10 of 15, EHL Maths & Excel final (AP)
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Successive % changes
When a value changes several times in a row, each change applies to the new value. So you multiply the (1+r) factors; you never add the rates.
When the exam asks for it
- “then”, “the following year”, “after two successive changes”
Formulas
Final value
Kt = Ko*((1+r1)*(1+r2)*(1+r3))Original value
Ko = Kt/((1+r1)*(1+r2)*(1+r3))Total change rate
r total = (1+r1)*(1+r2)*(1+r3) - 1Worked example
D2fx
=1000*(1+10%)*(1-10%)| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Case | Ko | Changes | Kt | |
| 2 | Up then down | 1,000 | +10%, -10% | 1000*1.1*0.9 = 990 | |
| 3 | Three changes | 1,000 | +5%, +8%, -4% | 1000*1.05*1.08*0.96 = 1,088.64 | |
| 4 | Find Ko | ? | +10%, +8% | 1188/(1.1*1.08) = 1,000 | |
| 5 |
Sheet1
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Step by step
=1000*(1+10%)*(1-10%)990, not 1,000=1000*(1+5%)*(1+8%)*(1-4%)1,088.64=1188/((1+10%)*(1+8%))1,000
⚠ Exam traps
- Never add the rates: +10% then -10% is not 0%, it is -1%.
- Write decreases as (1-r): -4% → 0.96.
Practice question
A price rises by 20% and then falls by 20%. What is the total change?
Show answer
✓ 1.2*0.8 = 0.96 → a 4% decrease.
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