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Solve Simple Interest Problems

In this worksheet, students will calculate simple interest, which assumes that the amount of money invested and the percentage rate of interest stays the same over time.

'Solve Simple Interest Problems' worksheet

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:  

Worksheet Overview

QUESTION 1 of 10

Do you want to make some money?

It would be surprising if you said "no"!

 

Then keep reading. So what happens when you invest money in a bank or building society?

It earns interest.

This means you make more money while your hard-earned cash sits in the bank!

 

Cartoon man with money

 

How to calculate simple interest:

We call it 'simple interest' as this assumes that both the amount of money invested and the percentage rate of interest stays the same over the years - unfortunately, not 'simple' as in easy! 

Let's look at an example to see this in action.

e.g. If we invest £300 for 4 years at an interest rate of 5% per annum, calculate the simple interest earned.

 

So the interest for one year is 5% of £300:

300 × 0.05 = £15

(This is the same calculation used to find a percentage of an amount of anything.)

 

Now we have £15 at the end of the year to go spend, and we haven't had to do a thing!

Assuming we take our £15 at the end of each year, how much will we have at the end of 4 years?

£15 × 4 = £60

 

Remember, we have not invested any more money, and the interest rate has stayed the same.

 

 Girl about to smash a piggy bank with a hammer

 

We are now going to raid the piggy bank and put our money in the building society!

 

If we invest £400 for 1.5 years at an interest rate of 6.5%, how much simple interest will we earn?

Interest for a year = 400 × 0.065 = £26

Interest for 6 months = £26 ÷ 2 = £13

Interest for 1.5 years = £26 + £13 = £39

 

 

Sometimes people take a fall as they don't understand simple interest.

If we are going to borrow money, we don't earn interest, we have to pay it instead!

The interest is calculated in the exact same way, but we will be owing money to the bank in this scenario. 

In this activity, we will calculate simple interest using the method above, which assumes that the amount of money invested and the percentage rate of interest stays the same over time.

Jackie takes out a loan of £130 for 3 years.

The rate of interest is charged at 6%.

 

How much interest does Jackie pay in total?

£7.80

£23.40

£15.60

£21.32

A family in a tent

 

Hugh and Mari wanted to buy a tent for their family holidays, and they were hoping 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 3 years, they had exactly the right amount saved to buy the tent.

 

How much does the tent cost? 

£7.80

£23.40

£15.60

£21.32

Match up each investment and time period on the left with the correct interest earning on the right. 

Column A

Column B

Investment of £400 over 5 years at an interest ra...
£60
Investment of £250 over 4 years at an interest ra...
£262.50
Investment of £1250 over 7 years at an interest r...
£20
Investment of £945 over 4 years 6 months at an in...
£37.53
Investment of £231 over 3 years 3 months at an in...
£85.05

Consider the two options below, then select the option which you would prefer.

 

(Hint: That's probably the one which will earn you the most money!)

Invest £350 over 4 years at 3% interest

Invest £250 over 5 years at 3.5% interest

Stack of $100 bills

 

Jenny invests £675 in her bank account.

The bank pays interest of 5.5%.

 

Use this information to answer the questions below. 

Give your answer rounded to 2 decimal places.

Invest £350 over 4 years at 3% interest

Invest £250 over 5 years at 3.5% interest

A baby deer

 

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?

Invest £350 over 4 years at 3% interest

Invest £250 over 5 years at 3.5% interest

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

 

Give your answer to 2 decimal places.

Invest £350 over 4 years at 3% interest

Invest £250 over 5 years at 3.5% interest

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

 

Note, all answer options have been rounded to 1 decimal place.

4.5 years

4.6 years

4.4 years

4.3 years

Man grimacing at the camera and holding money

 

Harvey invests £2500 that earns 0.5% interest per month for the first 6 months.

After this point, the interest drops to 0.25% for the next 6 months.

 

How much interest did Harvey earn in the first year?

 

Give your answer to 2 decimal places.

4.5 years

4.6 years

4.4 years

4.3 years

Close-up of a red butterfly on a yellow flower

 

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

He gets a loan of £15,000 from the bank.

Mervyn does not want to pay more than £1,400 in interest.

 

If the interest rate is 3% per annum, how many years will he need to pay the interest back in to meet his goal?

2 years

3 years

4 years

5 years

  • Question 1

Jackie takes out a loan of £130 for 3 years.

The rate of interest is charged at 6%.

 

How much interest does Jackie pay in total?

CORRECT ANSWER
£23.40
EDDIE SAYS
First, let's calculate 1 year of interest: £130 × 0.06 = £7.80 Now we need to multiply this by 3 to find the interest for 3 years: £7.80 × 3 = £23.40 interest will be paid by Jackie over 3 years
  • Question 2

A family in a tent

 

Hugh and Mari wanted to buy a tent for their family holidays, and they were hoping 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 3 years, they had exactly the right amount saved to buy the tent.

 

How much does the tent cost? 

CORRECT ANSWER
EDDIE SAYS
This question may sound confusing, but we simply need to find the interest over this period which is the same amount as the cost of the tent. I years' interest: £1500 x 0.07 = £105 3 years' interest: £105 × 3 = £315 This is the same cost as the tent, so the tent costs £315. Luckily they earned just enough interest to pay for it!
  • Question 3

Match up each investment and time period on the left with the correct interest earning on the right. 

CORRECT ANSWER

Column A

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 years ...
£85.05
Investment of £231 over 3 years ...
£37.53
EDDIE SAYS
You will be an expert in calculating interest on your savings after matching these up! Let's work through each calculation, one at a time. 400 × 0.03 = £12 for 1 year 12 × 5 = £60 for 5 years 250 × 0.02 = £5 for 1 year 5 × 4 = £20 for 4 years 1250 × 0.03 = £37.50 for 1 year £37.50 × 7 = £262.50 for 3 years £945 × 0.02 = £18.9 for 1 year £18.9 x 4 = £75.60 for 4 years 6 months = £18.90 ÷ 2 = £9.45 4.5 years = £75.60 + £9.45 = £85.05 £231 × 0.05 = £11.55 for 1 year £11.55 × 3 = £34.65 for 3 years 3 months is 1/4 of the year, so £11.55 ÷ 4 = £2.89 3.25 years = £34.65 + £2.89 = £37.54
  • Question 4

Consider the two options below, then select the option which you would prefer.

 

(Hint: That's probably the one which will earn you the most money!)

CORRECT ANSWER
Invest £250 over 5 years at 3.5% interest
EDDIE SAYS
We need to compare these two scenarios and work out which is best for us! £350 × 0.03 = £10.50 for 1 year £10.50 × 4 = £42 for 4 years That's not a bad return, let's check out the other option now. £250 × 0.035 = £8.75 for 1 year £8.75 × 5 = £43.75 for 5 years That's even better! Let's go for the second option as it definitely provides the best return on our investment.
  • Question 5

Stack of $100 bills

 

Jenny invests £675 in her bank account.

The bank pays interest of 5.5%.

 

Use this information to answer the questions below. 

Give your answer rounded to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
This is a case of reading each question and thinking through the scenario described carefully. £675 × 0.055 = £37.125 for 1 year £37.125 × 3 = £111.38 (rounded to 2 d.p.) for 3 years £37.125 × 5 = £185.63 (rounded to 2 d.p.) for 5 years The final question looks trickier, but we simply need to add the interest earned to her original amount. £675 + £185.63 = £860.63 in total after 5 years Don't be tempted to add both the 3 and 5 years of interest, as this would give 8 years overall. Wouldn't that be nice if the bank made that kind of mistake?
  • Question 6

A baby deer

 

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?

CORRECT ANSWER
EDDIE SAYS
Did you have no i-DEER on this one? Okay, you groan, very punny! ;-) The way to work out these sorts of problems is just the same as calculating simple interest; remember it's not always about money! 1250 × 0.08 = 100 new deer born per year. 100 × 3 = 300 new deer born in 3 years.
  • Question 7

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

 

Give your answer to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
This sounds complicated, but we just need to take it one step at a time. Interest for 1 year would be 11% of £850: £850 × 0.11 = £93.50 We are asked when the interest will reach £200, which we can calculate like this: £200 ÷ £93.50 = 2.139 years = 2.14 years, when rounded to 2 d.p. This is one of those trickier questions that wants us to take our knowledge one step further - don't worry, we are up to the challenge!
  • Question 8

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

 

Note, all answer options have been rounded to 1 decimal place.

CORRECT ANSWER
4.4 years
EDDIE SAYS
Let's follow the same process again here. £1500 × 0.06 = £90 interest per year £400 ÷ £90 = 4.4 years You're almost ready to start charging your friends and family to work out their investments!
  • Question 9

Man grimacing at the camera and holding money

 

Harvey invests £2500 that earns 0.5% interest per month for the first 6 months.

After this point, the interest drops to 0.25% for the next 6 months.

 

How much interest did Harvey earn in the first year?

 

Give your answer to 2 decimal places.

CORRECT ANSWER
EDDIE SAYS
Only Harvey could make such a bad investment! Working this out takes quite a lot of thought, so take your time. We need to work out the interest for 6 months in this case, not a full year. We calculate this by finding a year and halving our answer: 2500 × 0.005 × 0.5 = £6.25 Let's do the same thing to find the interest in the second 6 months: 2500 × 0.0025 × 0.5 = £3.125 Now we just need to add these amounts together to find the full years' interest: £6.25 + £3.125 = £9.375 = £9.38 to 2 d.p.
  • Question 10

Close-up of a red butterfly on a yellow flower

 

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

He gets a loan of £15,000 from the bank.

Mervyn does not want to pay more than £1,400 in interest.

 

If the interest rate is 3% per annum, how many years will he need to pay the interest back in to meet his goal?

CORRECT ANSWER
3 years
EDDIE SAYS
Let's start by finding the interest which will be paid in a year, as usual: £15000 × 0.03 = £450 interest per year Now we can divide Mervyn's goal of £1400 by this amount: £1400 ÷ £450 = 3.1111... years Mervyn definitely does not want to exceed this amount, so he would need to pay the money back within 3 years to ensure this. You can now calculate simple interest, which assumes that the amount of money invested and the percentage rate of interest stays the same over time - well done, you'll be beating the bank in no time!
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