Simple & Compound Interest, Growth & Decay (Cambridge IGCSE Maths): Revision notes

Section 1

How do I calculate simple interest?

Simple interest is calculated only on the original amount (the principal) each year — it does not grow on top of previous interest.

$\text{Simple Interest} = \frac{P \times R \times T}{100}$

where P = principal, R = rate (%), T = time (years).

Example: $500 invested at 4% simple interest for 3 years. Interest = (500 x 4 x 3) / 100 =$ 60

Key termssimple interestprincipal

Section 2

How do I calculate compound interest?

Compound interest is calculated on the current total each year, so interest is earned on previous interest too.

$\text{Total} = P \left(1 + \frac{R}{100}\right)^n$

where P = principal, R = annual rate (%), n = number of years.

Example: $500 invested at 4% compound interest for 3 years. Total =$ 500 \times 1.04^3 = $562.43 $Interest earned =$ 562.43 - 500 = $62.43$

Note this formula is not always given in the exam — you are expected to know it.

Key termscompound interest

Exam tip

Compound interest is simply repeated percentage increase — use the multiplier method: multiply by (1 + R/100) once for each year.

Section 3

How do I solve repeated percentage change problems? (Extended)

Repeated percentage change situations (compound interest, depreciation, population growth) all use the same multiplier structure:

$\text{Final amount} = \text{Initial amount} \times (\text{multiplier})^n$

Use a multiplier greater than 1 for growth, and less than 1 for decay/decrease.

Example: A car worth $12,000 depreciates by 15\% per year. Value after 4 years =$ 12000 $\times$ 0.85^4 = $6264.19$

Key termsdepreciation

Section 4

How do reverse percentages work? (Extended)

Reverse percentages find an ORIGINAL value when you're given a value AFTER a percentage change.

Method: Set the after-change amount equal to (original x multiplier), then divide.

Example: A jacket sells for $68 after a 20% discount. Find the original price. After discount = 80% of original, so 0.80 x original = 68 Original = 68 ÷ 0.80 =$ 85

Key termsreverse percentage

Common mistake

Do not simply add back the percentage to the final value (e.g. adding 20% of $68) — this is wrong because the percentage was originally taken of the ORIGINAL price, not the final one. Always divide by the multiplier instead.

Section 5

How is exponential growth and decay used in context? (Extended)

Exponential growth and decay follow the general form:

$y = ab^x$

where a is the starting value, b is the growth/decay multiplier, and x is time.

$b > 1$ : growth (e.g. population increase, investment growth)
$0 < b < 1$ : decay (e.g. depreciation, radioactive decay)

This is the same structure as compound interest and repeated percentage change — just written in function form.

Key termsexponential growthexponential decay

Must Know

Simple interest = (P x R x T) / 100, calculated only on the principal
Compound interest total = P(1 + R/100)^n, growing on the running total
Repeated percentage change: final = initial x (multiplier)^n
Reverse percentages: divide the after-change value by the multiplier to find the original
Growth uses a multiplier > 1; decay uses a multiplier between 0 and 1
Exponential model: y = ab^x, matching the compound interest structure

That's the notes covered.

Carry on to the next subtopic.