WJEC GCSE Maths
Topic questions Ratio, proportion and rates of change Growth & decay
15 questions · 89 marks · about 2 hours
Bethan bought a house in January 2000 for £30 000.
In the first 10 years, her house increased in value each year by 6% of its previous year’s value. In the following 15 years, her house increased in value each year by 11% of its previous year’s value.
Calculate the value of Bethan’s house in January 2025.
Menna is going to invest £400 in her bank’s savings account.
The savings account has a special interest rate for one year only.
The account pays 0∙2% interest per month for the first 10 months, and then 1∙7% interest per month for the last 2 months of the year.
Calculate the AER the bank should be advertising on the account.
Give your answer as a percentage, correct to 2 decimal places.
Delia bought a gold bracelet at a car boot sale a few years ago.
Delia’s bracelet has increased in value by 40%. Her gold bracelet is now worth £42.
Calculate how much Delia paid for the bracelet in the car boot sale.
The Cardiff Saver account pays interest at a rate of 0.6% every 3 months. Evan invests £5000 in this account.
Evan does not make any further deposits or withdrawals after opening the account. Calculate how much money is in the account after 4 
years.
The Pontypridd Saver account has an AER of 4%. The account pays interest every 6 months. Myles invests money in this account.
Calculate the interest rate that is applied to the account every 6 months. Give your answer as a percentage correct to 2 decimal places.
You must show all your working.
On 1st April 2023, Caitlin invested £10 000 into a savings account. The account had a nominal annual interest rate of 3%, with interest paid on the last day of every month. Caitlin did not plan to make any further payments into the account or make any withdrawals.
Calculate the date when Caitlin will first have over £10 500 in her account.
Date when Caitlin will first have over £10 500 in her account is
Calculate the AER for Caitlin’s savings account.
Give your answer as a percentage, correct to 2 decimal places.
On 1st January 2022, Jay invested £850 in the Savrplus savings account with ‘Banc y Ddraig’. The Savrplus account pays interest at a rate of 0∙48% every month. The interest is paid on the last day of every month. Jay does not plan to withdraw any money or make any further payments into the account.
Calculate the date when Jay will first have over £1000 in his account.
Date when Jay will first have over £1000 in his account is........
Imogen has £2000 to invest.
Details of two savings accounts are shown below.
If Imogen invested the £2000 in the Online Saver account, how much money would be in the account after 30 days?
You must show all your working.
Calculate the AER for the Platinum Plus account.
Give your answer as a percentage correct to 2 decimal places.
On 1st January 2017, Samantha and Dyfan invested money into different savings accounts.
They did not make any further payments into their accounts or withdraw any money from their accounts.
Samantha invested £2000 in a savings account that paid interest at a rate of 0∙95% every 3 months.
Show that Samantha would have £2038.18 in the account after 6 months.
Dyfan invested £3000 in a savings account that paid interest at a rate of 1∙02% every 3 months. Interest is paid on the last day of each 3-month period.
Calculate the date when Dyfan will first have over £3600 in his account.
Date when Dyfan will first have over £3600 in his account is…………........ ……………
Cellan is planning to invest a sum of money into a savings account.
Cellan has picked up a leaflet describing an account offered by a local bank. The details of the account are shown below.
Calculate the Annual Equivalent Rate (AER) that The Gower account is offering.
Give your answer as a percentage.
Give one reason why banks use AER.
Cellan decides to invest his savings of £3000 into a ‘Gower’ savings account. He plans to save enough money to buy a motorbike costing £3200.
Calculate how much short of the £3200 Cellan would be after 1 year.
Kingsley invests £3000 in an account that pays 2% compound interest per annum. He does not make any further payments into his account. He does not withdraw any money from his account.
How much will Kingsley have in his account after two years?
Amount in Kingsley’s account after two years is £........
Kingsley buys a portable Bluetooth speaker. The speaker has been reduced by 20% in a sale. He pays £72 for the speaker in the sale.
What was the original price of the speaker?
Original price of the speaker is £........
Kingsley invests £3000 in an account that pays 2% compound interest per annum. He does not make any further payments into his account. He does not withdraw any money from his account.
How much will Kingsley have in his account after two years?
Amount in Kingsley’s account after two years is £........
Kingsley buys a portable Bluetooth speaker. The speaker has been reduced by 20% in a sale. He pays £72 for the speaker in the sale.
What was the original price of the speaker?
Original price of the speaker is £........
Circle either TRUE or FALSE for each statement given below.
| STATEMENT | ||
| A nominal annual interest rate is not the same as an AER. | TRUE | FALSE |
| A savings account offers a nominal annual interest rate of 2%, with interest paid monthly. After a year, any investment will have increased in value by exactly 2%. | TRUE | FALSE |
| A savings account offers an AER of 2.4%, with interest paid monthly. The monthly interest rate the account offers will be exactly 0.2%. | TRUE | FALSE |
| £100 is invested in a savings account that pays monthly interest at a rate of 1%. There are no further transactions into or out of the account. The amount in the account after a year will be £112. | TRUE | FALSE |
Benjamin invests £1000 into an account that pays interest every 6 months. He does not make any further payments into the account, and does not withdraw any money either. After a year, there is £1036 in the account.
Calculate how much was in the account after 6 months. Give your answer correct to the nearest penny.
You must show all your working.
Iestyn opened a savings account on 1 August 2017, investing £2800.
On 1 October 2017, he viewed his savings account online. The table below shows all the transactions that had taken place since he opened the account.
| Date | Details | Paid in (£) | Paid out (£) | Balance (£) |
| 01/08/17 | Account opened | 2800.00 | 2800.00 | |
| 31/08/17 | Interest | 14.00 | 2814.00 | |
| 30/09/17 | Interest | 14.07 | 2828.07 |
Calculate the nominal interest rate per annum.
Calculate the AER the account was paying.
Give your answer as a percentage, correct to 2 decimal places.
Huw wants to open a savings account.
Here are the details of savings accounts advertised by two local Welsh banks.
What is 1∙98% as a decimal?
Circle your answer.
0∙0198 0∙198 1∙098 1∙98 98∙0
Which of these two banks should Huw choose in order to gain the most interest per annum?
You must show your working.
Interest earned from savings is taxable, according to the table below.
Matthew is a higher rate taxpayer. Therefore, any savings interest he earns over £500 within a year is taxed at 40%.
On 1st May 2016, he invested £150 000 in a savings account that pays interest at a rate of 1∙98% per annum.
What is this interest rate per month, written as a decimal?
Circle your answer.
0∙0033 0∙00495 0∙00165 0∙0099 0∙0066
Savings interest is added at the end of every month.
Calculate the date when the interest that Matthew earned went above his annual tax-free limit, and the amount of tax he would have to pay on this interest if he had
closed the account on this date.
Date........ Tax Matthew would have to pay........
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