Determine ThisGrade 11 Finance Growth Decay — How to Identify the Question Type
Grade 11 Finance questions all use the same two underlying formulas — simple growth/decay and compound growth/decay — but disguise which one applies behind different words. Before you reach for a formula, work out whether the amount changes by a fixed amount each period (simple) or by a fixed percentage of the current amount each period (compound), and whether it's growing or shrinking.
Type 1: Simple interest / simple decay
Trigger words: "Simple interest", "straight-line depreciation", "interest is not compounded"
Trigger structure: The interest amount or the decrease is calculated on the ORIGINAL amount every period, not on the new balance.
Do not confuse with: Compound interest (Type 2) — simple interest grows by the same fixed amount each year; compound interest grows by a changing amount each year.
Method (no numbers — just the steps)
- Identify P (the original amount), i (the rate as a decimal), and n (the number of periods)
- Substitute into A = P(1 + in) for growth, or A = P(1 − in) for decay
- Solve for whichever value the question asks for
See the progression — same type, increasing difficulty
Type 2: Compound interest / compound decay
Trigger words: "Compound interest", "compounded annually/monthly", "the value depreciates by r% of its value each year"
Trigger structure: The interest or decrease each period is calculated on the CURRENT (already-grown or already-shrunk) balance, not the original amount.
Do not confuse with: Simple interest (Type 1) — look for the word 'compound', or for a rate applied 'each year of its value' (which implies the changing balance).
Method (no numbers — just the steps)
- Identify P, i (as a decimal) and n
- Substitute into A = P(1 + i)ⁿ for growth, or A = P(1 − i)ⁿ for decay
- Solve for whichever value is unknown
See the progression — same type, increasing difficulty
Type 3: Nominal vs effective interest rates
Trigger words: "Nominal annual interest rate", "effective annual interest rate", "compounded monthly/quarterly"
Trigger structure: Appears whenever interest is compounded MORE often than once a year — the rate quoted (nominal) is not the rate the money actually earns over a full year (effective).
Do not confuse with: A plain compound interest question (Type 2) where compounding is annual — nominal vs effective only matters when compounding happens monthly, quarterly, etc.
Method (no numbers — just the steps)
- Identify the nominal annual rate and how many times per year it compounds (m)
- Substitute into the effective rate formula: i_eff = (1 + i_nom/m)^m − 1
- Convert the result to a percentage
See the progression — same type, increasing difficulty
Type 4: Combination growth and decay (two-phase) problems
Trigger words: "...for the first n years... thereafter...", a value that grows for one period then changes rate or type partway through
Trigger structure: Two (or more) separate growth/decay periods chained together — the end value of the first period becomes the starting value of the second.
Do not confuse with: A single compound growth question (Type 2) — the giveaway here is a CHANGE described partway through the timeline (a different rate, or a switch from growth to decay).
Method (no numbers — just the steps)
- Split the timeline into separate phases at the point where the rate or type changes
- Calculate the value at the end of the first phase
- Use that result as the starting value (P) for the next phase
- Repeat for each phase, then read off the final value
See the progression — same type, increasing difficulty
Words like determine and hence appear throughout this topic — see the instruction word glossary for full definitions.