KS3 Maths · Year 8 · Chapter 1: Percentages · Lesson 1

Simple interest

Year 8About 70 minutesCalculator allowed55 marks

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Quick questions to start.

A1
Needed today
Work out $15%$ of $£60$ .
[1 mark]
Answer
A2
Needed today
Write $0.035$ as a percentage.
[1 mark]
Answer
A3
Year 7
Increase $£80$ by $15%$ .
[1 mark]
Answer
A4
Year 7
Solve $4 x - 7 = 29$ .
[1 mark]
Answer

Example, then your turn

Year 8

Simple interest is the same percentage of the ORIGINAL loan each time. Your teacher works through each example with you. Then try the one beside it.

Example 1

Asha takes a loan of $£720$ . She pays simple interest of $4%$ each month for $9$ months. Work out the total interest she pays.

Hint Work out

4%

of the loan once. She pays that amount every month.

B1
Dev takes a loan of $£1350$ . He pays simple interest of $3%$ each month for $8$ months. Work out the total interest he pays.
[2 marks]
Answer

Example 2

Ellis borrows $£2400$ . He pays simple interest of $2.5%$ every three months for $2$ years. Then he pays back the loan. How much does he pay altogether?

Hint Count the payments: there are

4

lots of three months in a year. Add the loan to the interest.

B2
Grace borrows $£3600$ . She pays simple interest of $1.5%$ each month for $3$ years, then pays back the loan. Work out (i) the total interest, (ii) the total amount she pays.
[3 marks]
Answer(i) $£ \dots\dots$ (ii) $£ \dots\dots$

Example 3

Hana has a loan of $£850$ . She pays interest of $£23.80$ each month. What is the monthly rate of simple interest?

Hint Write the interest as a fraction of the loan, then change it to a percentage.

B3
Isaac has a loan of $£1240$ . After $4$ months he has paid a total of $£148.80$ simple interest. Work out the monthly rate of interest.
[3 marks]
Answer

Example 4

Jade borrows $£640$ at $0.75%$ simple interest each week. After how many weeks has she paid $£72$ interest?

Hint Work out the interest for one week. How many of those make

£72

B4
Kofi borrows $£2250$ at $1.2%$ simple interest each month. After how many months has he paid $£432$ interest?
[2 marks]
Answer

Example 5

Lena pays simple interest of $3.5%$ each year on a loan. After $6$ years she has paid $£1680$ interest. How much did she borrow?

Hint In

6

years she pays

6 \times 3.5%

of the loan. That percentage of the loan is

£1680

B5
Marc pays simple interest of $2.5%$ each month on a loan. After $16$ months he has paid $£1380$ interest. Work out how much he borrowed.
[3 marks]
Answer

Practice

Year 8

C1
Kira borrows $£3200$ at $2.25%$ simple interest each month for $10$ months. Leon borrows $£4200$ at $1.5%$ simple interest each month for a year. Who pays more interest, and by how much?
[3 marks]
Answer
C2
Nia borrows $£960$ at $0.8%$ simple interest each month for $2$ years. What percentage of the loan is the total interest?
[2 marks]
Answer

C3
Omar has a loan of $£1800$ . He pays simple interest of $0.2%$ each week. How much interest does he pay in one year of $52$ weeks?
[2 marks]
Answer
C4
The total amount $A$ paid back on a loan of $£ P$ at $R %$ simple interest for $T$ payments is $A = P (1 + \frac{R T}{100})$ . Work out $A$ when $P = 1500$ , $R = 1.8$ and $T = 20$ .
[2 marks]
Answer
C5
Pia borrowed $£2600$ . After $12$ months of simple interest she paid back $£3341$ altogether. Work out the monthly rate of interest.
[3 marks]
Answer
C6
Ravi puts $£640$ in a savings account that pays $2.5%$ simple interest each year. How much is in the account after $4$ years?
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Jo borrows $£1500$ at $4%$ simple interest each year for $3$ years. Jo says, "After the first year I owe $£1560$ , so in the second year I pay $4%$ of $£1560$ ."
Explain why Jo is wrong. Work out the total interest Jo pays.
[3 marks]
AnswerTotal interest $£ \dots\dots$

D2
Sophie wants to borrow $£6000$ for $3$ years. The table shows two offers.
(a)
Work out the total interest Sophie would pay to Arden Bank.
[2 marks]
Answer
(b)
Which offer costs Sophie less in total? You must show your working.
[3 marks]
Answer
Total for D2: 5 marks
D3
Tia has a loan of $£1500$ . The graph shows the total simple interest she has paid after each month.
(a)
Write down the total interest she has paid after $4$ months.
[1 mark]
Answer
(b)
Work out the monthly rate of simple interest.
[2 marks]
Answer
(c)
The loan lasts until she has paid $£345$ interest. How many months is this?
[2 marks]
Answer
Total for D3: 5 marks
D4
Sam pays simple interest of $1.5%$ each month on a loan. After $2$ years he has paid $£1260$ interest.
(a)
Work out how much Sam borrowed.
[3 marks]
Answer
(b)
Work out the total amount Sam pays, the loan and the interest together.
[1 mark]
Answer
Total for D4: 4 marks
D5
Priya borrows $£900$ . She pays it back in $12$ equal monthly payments. The payments include simple interest of $2%$ of the loan each month. Work out the amount of each monthly payment.
[3 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A shop offers two ways to borrow money for $2$ years. Plan A: simple interest of $1.5%$ of the loan each month. Plan B: simple interest of $15%$ of the loan each year, plus a fixed fee of $£60$ . For what size of loan do the two plans cost the same?
[4 marks]
Hint 1 · What to try
Call the loan $£ P$ and write the cost of each plan in terms of $P$ .
Hint 2 · The first line
Plan A: $24 \times 1.5% = 36%$ , so $0.36 P$ . Plan B: $2 \times 15% = 30%$ , so $0.30 P + 60$ .
Hint 3 · The full method
$0.36 P = 0.30 P + 60$ , so $0.06 P = 60$ and $P = 1000$ . Check: both cost $£360$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out simple interest for any number of payments.
I can find the rate or the number of payments from the interest.
I can find the size of a loan from the interest paid.
I can compare two loans and choose the one that costs less.

Answers and mark scheme

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