Simple interest is always calculated on the original amount.

Compound interest is the interest calculated on the original amount and the interest accumulated over the previous period.

When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

Advanced problem solving with percentages

Maths

Checking and securing understanding of percentage increase

Checking and securing understanding of percentage decrease

Percentage profit and loss

Simple and compound interest

Simple interest calculations

Simple interest calculations with technology

Compound interest calculations

Compound interest calculations with technology

Calculating compound interest rates

Changing compound interest rates

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. This unit ensures pupils have had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

In the prior unit, pupils developed the skills to calculate a given percentage of an amount. In this unit, these skills are extended to performing simple and compound interest calculations.

In this unit pupils will learn how to perform simple and compound interest calculations using percentages.

Percentages

A bank offers compound interest of 3% for the first 2 years, followed by 2% for the final year. If I invest £5000 at the start, how much money will I have at the end?

Square A has sides 50% larger than square B.

Square B has sides 50% larger than square A.

Square A has sides 75% larger than square B.

Square B has sides 100% larger than square A.

A square (A) has an area of $$36cm^2$$ and a second square (B) has an area of $$144cm^2$$. What is the percentage difference in side length between square A and square B?  

A toy is reduced in price by 10%, then a further 10% on the new price a week later. What is the percentage decrease overall from the original price? 

A bank offers compound interest of 5% for the first 2 years, followed by 2% for the final year. If I invest £10 000 at the start, how much money will I have at the end?

This is a coincidence and is only true for this example. 

Reversing percentages in this way always works.

Aisha declares that "40% of 26 is the same as 26% of 40". Which statement below is correct? 

A 500g box of cereal (A) costs £2.60.  A larger 1300g box (B) costs £6.76. Which is the best value for money? 

If a number increases by 22% and is now 34.16, what was it originally? 

A mathematician celebrates their shares increasing by 18% which are now worth £649. How much did they originally invest?

If I decrease £105 to £21, what is the percentage loss? 

A good investment gains value by 9% each year. If the investment was worth £20 000 when purchased how much is it worth after 3 years? 

Advanced problem solving with percentages

Lesson outcome