# Solve Simple Interest Problems

In this worksheet, students will be able to calculate simple interest problems.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Discrete Growth and Decay

Difficulty level:

### QUESTION 1 of 10

Do you want to make some money?

I would be surprised if you said no.

What happens when you invest money in a bank or building society?

You gain interest (this means you earn money while your hard earned cash is in the bank)

Simple Interest

This is calculated by assuming the amount of money invested stays the same over the years and that the percentage rate of interest stays the same.

You invest £300 for 4 years at an interest rate of 5% per annum.  (This means per year).

Calculate the simple interest earned.

Interest for 1 year is 5% of £300

To find this 300 x 0.05 = £15.  This is the same calculation used to find a percentage of an amount of anything.

You now have £15 pound at the end of the year to go an spend, and you haven't had to do anything!!

Assuming you take your £15 at the end of each year how much will you have at the end of 4 years?

£15 x 4 = £60.   remember you haven't invested any more money and the interest rate has stayed the same.

You are now going to raid the piggy bank to put your money in the building society.

You invest £400 for 1 1/2 years at an interest rate of 6 1/2%.  Find the simple interest earned.

Interest for 1 year = 400 x 0.065 = £26

Interest for 6 months = £26 ÷ 2 = £13

Interest for 1 1/2 years is £26 + £13 = £39

Sometimes people take a fall as they don't understand simple interest.  If you are going to borrow money, you have to PAY interest.

The interest is calculated in the same way,  but you will be owing money to the bank!!  I suppose that is fair...

You take out a loan of £130 for 3 years.  The rate of interest charged at 6%.  How much interest did you pay in total?

£7.80

£23.40

£15.60

£21.32

Hugh and Mari wanted to buy a tent for the family holidays.

They were going to use the interest from their savings to buy it.

They invested £1500 at the bank with an interest rate of 7%.

At the end of three years they had enough to buy the tent.

How much interest did they earn over the period of the investment?

Match up the these calculations

## Column B

Investment of £400 over 5 Years at an interest ra...
£85.05
Investment of £ 250 over 4 years at an interest r...
£20
Investment of £1250 over 7 years at an interest r...
£262.50
Investment of £945 over 4 1/2 years at an interes...
£60
Investment of £231 over 3 years 3 months at an in...
£37.53

Would you rather

Investment of £350 over 4 years at 3%

Investment of £250 over 5 years at 3.5%

Jenny invests \$675 in her bank account.

The bank pays interest of 5.5%.

Investment of £350 over 4 years at 3%

Investment of £250 over 5 years at 3.5%

The deer population in the local forest is 1250.

Each year the population increases by 8%.

How many new deer have been born into the population after 3 years?

Calculate how long it would take for an invested sum of £850 to produce £200 simple interest at 11% per annum.(per year)

How long would it take for an invested sum of £1500 to produce £400 simple interest at 6% per annum?

4.5

4.6

4.4

4.3

Harvey invests £2500 that earns 0.5% per month for the first 6 months and then the interest drops to 0.25% for the next 6 months.

How much interest did Harvey earn in that year?

Mervyn takes out a loan to set up a rare species butterfly farm.

He gets a loan of £15,000 from the bank.  He doesn't want to pay more than £1400 interest. If the interest rate is 3% per annum, in how many years will he need to pay back the loan?

2

3

4

5

• Question 1

You take out a loan of £130 for 3 years.  The rate of interest charged at 6%.  How much interest did you pay in total?

£23.40
EDDIE SAYS
First calculate 1 years interest. £130 x 0.06 = £7.80 £7.80 x 3 = £23.40 You can see why it is called simple interest can't you.
• Question 2

Hugh and Mari wanted to buy a tent for the family holidays.

They were going to use the interest from their savings to buy it.

They invested £1500 at the bank with an interest rate of 7%.

At the end of three years they had enough to buy the tent.

How much interest did they earn over the period of the investment?

£315
EDDIE SAYS
Thats a big tent for the sort of money. They earned interest as follows I year interest would be £1500 x 0.07 = £105 3 years interest would be £315 Remember to read through the whole question to get all the information you need.
• Question 3

Match up the these calculations

## Column B

Investment of £400 over 5 Years ...
£60
Investment of £ 250 over 4 years...
£20
Investment of £1250 over 7 years...
£262.50
Investment of £945 over 4 1/2 ye...
£85.05
Investment of £231 over 3 years ...
£37.53
EDDIE SAYS
This is designed to get you used to the calculation by applying it multiple times. At least you will be an expert in calculating interest on your savings. 400 x 0.03 = £12 for 1 year 12 x 5 = £60 for 5 years 250 x 0.02 = £5 for 1 year 5 x 4 = £20 for 4 years 1250 x 0.03 = £37.50 for 1 year = £37.50 x 7 = £262.50 for 3 years. £945 x 0.02 = £18.9 for 1 year £18.9 x 4 =£75.60 for 4 years. 6 months = £18.90÷ 2 = £9.45. £75.60 + £9.45 =£85.05 £231 x 0.05 =£11.55 £11.55 x 3 = £34.65 for 3 years 3 months is 1/4 of the year so £11.55÷4 =£2.89 £34.65 + £2.89 = £37.54
• Question 4

Would you rather

Investment of £250 over 5 years at 3.5%
EDDIE SAYS
So let us see £350 x 0.03 = £10.50 x 4 = £42. Not bad £250 x0.035 = £8.75 x 5 = £43.75 Even better
• Question 5

Jenny invests \$675 in her bank account.

The bank pays interest of 5.5%.

EDDIE SAYS
This is a case of reading the question and thinking about this carefully. \$675 x 0.055 = \$37.125 x 3 = \$111.38 (2.d.p) \$675 x 0.055 = \$37.125 x 5 = \$185.66 (2 d.p) Now here's the thing. You only need to add the interest after 5 years to the original amount. \$675 + \$185.66 = \$860.66 Don't be tempted to add in the 3 and 5 years. This would give 8 years. Wouldn't that be nice if the bank made that mistake.
• Question 6

The deer population in the local forest is 1250.

Each year the population increases by 8%.

How many new deer have been born into the population after 3 years?

300
EDDIE SAYS
Did you have no idea on this one? Get it? Okay you can groan. The way to work out these sorts of problems is the same as calculating simple interest. It is not always about money. 1250 x 0.08 = 100 100 x 3 = 300
• Question 7

Calculate how long it would take for an invested sum of £850 to produce £200 simple interest at 11% per annum.(per year)

2.14 years
EDDIE SAYS
Interest for 1 year would be 11% of £850 £850 x 0.11 = £93.50 £200 ÷ £93.50 = 2.139 years (2.14) This is one of those awkward questions that wants you to take your knowledge that one step further. But this is nothing you can't do
• Question 8

How long would it take for an invested sum of £1500 to produce £400 simple interest at 6% per annum?

4.4
EDDIE SAYS
Just apply what you know. £1500 x 0.06 = £90 per year £400 ÷ £90 = 4.4 years You should start charging your friends to work out their investments.
• Question 9

Harvey invests £2500 that earns 0.5% per month for the first 6 months and then the interest drops to 0.25% for the next 6 months.

How much interest did Harvey earn in that year?

£9.38
EDDIE SAYS
Only Harvey could make such a bad investment. This takes quite a lot of thought 2500 x 0.005( 1/2%) not 0.05 (5%) so be careful 2500 x 0.005 = £12.50 Hurrah. Oh wait a minute that would be for 1 year not 6 months. 6 months would be £12.50 ÷ 2 = £6.25 2500 x 0.0025 (1/4%) = £6.25 for 1 year. 6 months is £6.25 ÷ 2 = £3.125 £6.25 +£3.125 = £9.375 (£9.38 to 2 d.p)
• Question 10

Mervyn takes out a loan to set up a rare species butterfly farm.

He gets a loan of £15,000 from the bank.  He doesn't want to pay more than £1400 interest. If the interest rate is 3% per annum, in how many years will he need to pay back the loan?

3
EDDIE SAYS
£15,000 x 0.03 = £450 interest per year This is just a case of multiplying up now. £450 x 2 = £900 within 2 years £450 x 3 = £1350 within 3 years. Multiplying up again would take us over the £1, 400 that Mervyn wanted to pay in interest. Hence he should pay the loan back within 3 years.
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