Home

Maths

Ratio proportion and rates of change

Compound growth and decay

Compound growth and decay

Videos

Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Double brackets: Expanding and factorising

Double and triple brackets - Higher

Solving equations

Expressions, equations, formulae, functions and identities

Writing formulae and equations from word problems

Writing formulae and equations from diagrams

Rearranging formulae

Factorising quadratics

The quadratic formula - Higher

Complete the square - Higher

Algebraic fractions - Higher

Sequences

Finding the nth term

Solving inequalities

Inequalities on graphs - Higher

Iteration - Higher

Simultaneous equations: elimination and substitution

Non-linear simultaneous equations - Higher

Algebraic proof - Higher

Composite and inverse functions - Higher

Number

Types of numbers

Order of operations: BODMAS

Multiplying and dividing by powers of 10

Multiplying and dividing whole numbers

Multiplying and dividing decimals

Negative numbers: add, subtract, multiply, divide

Prime numbers and prime factorisation

Multiples, factors and prime factors

LCM and HCF

Fractions

Fractions, decimals and percentages

Writing recurring decimals as fractions

Rounding: Integers, decimal places, significant figures

Estimation

Error intervals

Upper and lower bounds - Higher

Powers and roots: Square and cube numbers

Laws of indices: multiply, divide, brackets

Index laws: negative and fractional indices - Higher

Surds: Simplify, add and subtract - Higher

Rationalising surds - Higher

Standard form calculations

Explainer Video

Tutor: Alice

Summary

Compound growth and decay

​​In a nutshell

Compound growth and decay (commonly used to work out compound interest) involves percentage changes over a period of time - usually on a yearly basis. 



Compound growth and decay formula

In order to calculate compound growth and decay, a formula must be used:


​Amount after n time=initial amount×(percentage change multiplier)n\text{Amount after n time} = \text{initial amount} \times \text{(percentage change multiplier)}^nAmount after n time=initial amount×(percentage change multiplier)n


This is sometimes written as:

​N=N0×(multiplier)nN = N_0 \times (\text{multiplier})^nN=N0​×(multiplier)n​​



Note: n could be time in years, months, days or any time period you can think of!


Example 1

Mitchell bought a car for £10,500£10,500£10,500. It depreciates in value by 12%12\%12% each year. How much will the car be worth in six years time?


Work out the multiplier.

1−0.12=0.881-0.12=0.881−0.12=0.88


Use the formula.

Amount after six years =10500×(0.88)6=£4876.24‾= 10500\times(0.88)^6 = \underline{£4876.24}=10500×(0.88)6=£4876.24​ (rounded to two decimal places.)​

​

Example 2

The panda population is decreasing by two percent every year. The current population is 500050005000. What was the population three years ago? (Round your answer to the nearest whole number).


Work out the multiplier.

1−0.02=0.981-0.02=0.981−0.02=0.98​​


Fill in the formula with what you know where xxx is the population three years ago.

7500=x×(0.98)37500=x\times(0.98)^37500=x×(0.98)3​​


Rearrange and solve for xxx.

7500=x×(0.98)3÷(0.98)3÷(0.98)37968.62=x\begin {aligned}&&7500&=x\times(0.98)^3 \\\div(0.98)^3&&&&\div (0.98)^3 \\&&7968.62&=x\end {aligned}÷(0.98)3​​75007968.62​=x×(0.98)3=x​÷(0.98)3​


Round to the nearest whole number.

​7968.62⇢7969‾7968.62 \dashrightarrow \underline{7969}7968.62⇢7969​


The population three years ago was 7969‾\underline{7969}7969​ pandas.​

​



Read more

Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Calculating percentages of amounts

Calculating percentages of amounts

Percentage change

Percentage change

Jump Ahead

Score 80% to jump directly to the final unit.

This is the current lesson and goal (target) of the path

Compound growth and decay

Compound growth and decay

Final Test

Test reviewing all units to claim a reward planet.

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is the n in the compound growth formula?

In the compound growth formula, n could be time in years, months, days or any time period you can think of!

What is the formula for compound growth and decay?

The formula for compound growth and decay is: Amount after n time = initial amount × (percentage change multiplier) to the power of n, where n is time.

What is compound growth and decay?

Compound growth and decay (commonly used to work out compound interest) involves percentage changes over a period of time - usually on a yearly basis.

Beta

© 2020 - 2025 evulpo AG