Compound Interest & DepreciationEdexcel IGCSE Maths: Revision notes

Section 1

What is the difference between simple and compound growth?

Simple interest adds the same amount each year, always calculated on the original amount.

Compound interest adds a percentage of the current amount, so the interest itself earns interest.

Simple: $I = P \times r \times t$ (where $r$ is the rate as a decimal, $t$ is time in years)
Compound: the amount grows by the same percentage, not the same amount, every year

On exam papers, always check which method is asked for — mixing them up is one of the most common errors.

Key termssimple interestcompound interestprincipal

Common mistake

Do not calculate one year's simple interest and just multiply it by the number of years — that only works for simple interest, never for compound interest.

Section 2

How do I build a multiplier for repeated percentage change?

A multiplier converts a percentage change into a single decimal number you multiply by.

For growth (increase): $\text{multiplier} = 1 + \frac{r}{100}$

For decay (decrease): $\text{multiplier} = 1 - \frac{r}{100}$

Change	Multiplier
+3%	1.03
+12%	1.12
-5%	0.95
-20%	0.80

Once you have the multiplier, repeated percentage change over $n$ years is: $\text{Final amount} = P \times (\text{multiplier})^n$

Key termsmultipliergrowthdecay

Exam tip

Write the multiplier down first, before doing anything else — it stops you rushing into the wrong formula under time pressure.

Example

£2000 invested at 4% compound interest for 3 years: $2000 \times 1.04^3 = £2249.73$ (to 2 d.p.).

Section 3

How is compound interest applied to savings and loans?

The general compound interest formula is: $A = P\left(1 + \frac{r}{100}\right)^n$

where:

$A$ = final amount
$P$ = principal (starting amount)
$r$ = interest rate per year (%)
$n$ = number of years

To find the total interest earned, subtract the principal from the final amount: $\text{Interest} = A - P$

This same formula is used for loans, where the amount owed grows each year if it isn't repaid — the mathematics is identical, only the context (money owed rather than money saved) changes.

Key termsamountinterest ratenumber of time periods

Example

£5000 borrowed at 6% compound interest for 2 years: $A = 5000 \times 1.06^2 = £5618.00$ , so the interest owed is $£618.00$ .

Section 4

How does depreciation work, and can rates change each year?

Depreciation is the loss in value of an item (like a car or machine) over time, calculated the same way as compound interest but with a decay multiplier: $A = P\left(1 - \frac{r}{100}\right)^n$

Different rates each year: if the percentage change is not the same every year, you cannot use a single power — instead multiply by each year's multiplier in turn: $A = P \times m_1 \times m_2 \times m_3 \times \ldots$

This is common in exam questions that give a table of different annual rates, or combine one year of growth with another year of decay.

Key termsdepreciation

Think of it like this

Think of a multiplier as a dial you turn each year — turning it the same amount every time is compound interest, turning it by different amounts each year is just repeated multiplication with different dials.

Example

A car worth £18000 depreciates by 15% in year 1 and 10% in year 2: $18000 \times 0.85 \times 0.90 = £13770$ .

Section 5

How do I work backwards to find the original amount or the rate?

Finding the original principal (reverse percentage): if you know the final amount $A$ after $n$ years at rate $r$ , rearrange the formula: $P = \frac{A}{\left(1 + \frac{r}{100}\right)^n}$

Finding the rate: rearrange to isolate the multiplier, then convert back to a percentage: $\left(1 + \frac{r}{100}\right) = \sqrt[n]{\frac{A}{P}}$

Finding the number of years: use trial and improvement, or logarithms if the syllabus permits — try successive powers of the multiplier until $A$ is reached or exceeded.

Key termsreverse percentage

Common mistake

Do not simply reduce the final amount by $r\%$ to 'undo' a growth of $r\%$ — you must divide by the multiplier, not subtract the same percentage.

Must Know

Compound interest/depreciation formula: $A = P(1 \pm \frac{r}{100})^n$ — + for growth, − for decay
Always convert a percentage change to a multiplier before calculating: e.g. +8% → 1.08, −8% → 0.92
Different rates each year means multiplying by a different multiplier each year, not raising one multiplier to a power
Total interest/depreciation = final amount − original amount
To reverse a percentage change, divide by the multiplier (or the multiplier raised to the power $n$ ) — never subtract the percentage again
Round money answers to 2 decimal places unless told otherwise

That's the notes covered.

Carry on to the next subtopic.