Saving & Borrowing (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Exam Questions

• When Carly started work she had a student loan of £12 000

• She started work on January 1st 2014 with an annual salary of £17 000

• She has to make repayments to the Student Loan Company.

• Each year she has to repay 9% of everything she earns in excess of £16 365

• To model her annual repayments, Carly assumed that her salary would increase by £1500 each year.

• She set up a simple spreadsheet as shown below.

Write a formula for cell C4

Simple interest at 2% is added to Carly’s outstanding loan at the start of every year.

So, after the first year, the outstanding debt is:

£12 000 + interest of £240 – repayment of £57.15

Work out when Carly would first owe less than her original student loan of £12 000

Sally is planning a holiday in Canada.

On 1 May 2020, Sally invested £2000 in this savings account.

On 1 May 2023, she closed the account and used all the money to buy Canadian dollars.

The exchange rate was £1 = 1.68 Canadian dollars

Did Sally get more than 3500 Canadian dollars?
You must show your working.

During the holiday, Sally bought a handbag for 190 Canadian dollars.

She paid with her bank debit card.

The bank

    added a fee of 2.5% of the cost of the handbag

    used an exchange rate of £1 = 1.75 Canadian dollars.

Work out the total amount, in pounds, that Sally had to pay

Use Student Loans in the Preliminary Material.

Anya left university in 2010

In January 2023, she decides to repay the rest of her student loan in one year.

The SLC will continue to take the usual repayments each month from her salary. Anya wants to make 12 equal additional monthly payments to pay off the loan.     

Anya’s salary is £45000 per year.     

The SLC tells Anya she needs to repay £2705 in total in 2023 to pay off the loan.

Work out the additional monthly payment she must make to pay off the loan in 12 months.

Arzoo wants to borrow money to buy a new car.

Two companies offer loans.

Company A nominal interest rate of 9% with the interest calculated annually.
Company B nominal interest rate of 8.75% with the interest calculated monthly.

Which company offers the best Annual Equivalent Rate (AER)?
Use the Formula Sheet.
You must show your working.

Peter took out a mortgage for £150 000 at the end of December 2021

The annual interest is 3.6%, charged monthly.

His monthly payment is £920

At the end of each month, the interest is added then the payment is deducted.

The spreadsheet shows some information about the amount he still owes at the end of each month

Complete the spreadsheet.

Give each value to the nearest penny.

Work out the total amount of interest that Peter pays in the first six months

Peter wants to know what percentage of his original mortgage he has still to pay after these six months.

Choose the spreadsheet formula he can use to work this out.

Some years ago, Kelly invested £2000 in a savings account.

Since then, she has not withdrawn money from the account but interest has been added.

The total in the account is now £2319, correct to the nearest pound.

Complete the error interval for the total amount of interest, £I, that has been added to the account.

Answer __________________ __________________

Jessica invests an amount in a variable rate savings account.

The account receives compound interest at

2.4% per year for the first 2 years
then
3.1% per year for the next 5 years.

Jessica says,

“My investment will increase by 20.3%, because 2 × 2.4 + 5 × 3.1 = 20.3”

By calculating the correct percentage increase, show that she is wrong.

Use Student Loans in the Preliminary Material.

Samir started a four-year course at university in 2016

On 1 September 2020 he started a job on an annual salary of £36 000

On that day he owed £23 700 to the Student Loan Company.

He knows that

• interest on his student loan is charged at the RPI + 1%

• he will receive a pay rise of £1000 after one year of work

• the threshold for student loans will stay the same.

Work out how much he will owe on 1 September 2022

Assume that

interest is added to the loan annually on 31 August after the full year of repayments has been deducted
and
the RPI stays the same for the two years.

Here is an advert for loans.

Lucy wants a loan for £1200

She wants to pay back the loan in two equal instalments, with

the first instalment at the end of one year
and
the second instalment at the end of two years.

Work out the amount of each instalment.

Use the APR formula on the Formulae Sheet.

Give your answer to the neares

Answer £ ______________________

Use Student loans from the Preliminary Material.

Andrew started university in September 2015 and took out a student loan.

He graduated from university in July 2018 and started work with an annual salary of £18 000

He receives a pay rise of 5% every January and an inflationary increase of 2% every April.

The spreadsheet shows some information about his salary.

Choose the formula that gives the correct value for cell C4

Complete the spreadsheet.

Give each value correct to the nearest penny.

In which month and year will Andrew have to start paying back his student loan?

Work out Andrew’s first month’s student loan repayment.

Yasmin wants to save money for her newborn son to go to university when he is 18.

She wants to invest some money in a savings account so he will have at least £20 000 in 18 years’ time.

She opens a savings account at 5.5% compound interest per year for 18 years.

Work out the minimum amount she

Chris takes out a mortgage for £160 000
The mortgage has an interest rate of 0.2% per month.
Chris repays £710 per month.

The amount of mortgage outstanding at the end of the nth month, £A_n, is given by the iteration formula

A_n = 1.002A_n–1 – 710

where A₀ = 160 000

Complete the table to show the amount of mortgage outstanding at the end of each of the first 4 months.

Chris says,

“In these 4 months the total interest is more than £1200”.

Is he correct?
You must show your working.

Sarah needs a payday loan.

She wants to borrow £235 for a period of 6 days and then pay the loan and interest back in one payment.

She finds these two options.

Sarah uses the formulae sheet to work out the amount she would have to pay back to See You Through.

Which loan company would be the cheaper option for her?
You must show you