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ScotlandApplications of MathematicsSyllabus dot point

How do loans, credit cards and APR work, and how do you compare the true cost of borrowing?

Analysing loans, credit cards and other borrowing, calculating repayments and outstanding balances, understanding APR as a measure of the true cost of credit, and comparing borrowing options.

A focused answer to the SQA Higher Applications of Mathematics finance content on borrowing, covering loan repayments and outstanding balances, credit cards and minimum payments, APR as the true cost of credit, and comparing borrowing options.

Generated by Claude Opus 4.810 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. How a loan balance changes
  3. Credit cards and minimum payments
  4. APR: the true cost of credit
  5. Comparing borrowing options
  6. Try this

What this dot point is asking

The SQA wants you to analyse borrowing: calculate loan repayments and the outstanding balance month by month, understand how credit cards and minimum payments work, interpret APR as a measure of the true cost of credit, and compare borrowing options on a fair basis. Finance carries the most marks in the question paper, and borrowing is central to it.

How a loan balance changes

A loan is repaid by regular payments while interest accrues on what is still owed. Each period two things happen in order: interest is added to the balance, then the repayment is subtracted.

Because interest is charged on the reducing balance, early payments are mostly interest and later payments mostly principal. A spreadsheet column models this clearly, one row per period.

Credit cards and minimum payments

A credit card charges interest on the unpaid balance each month. The minimum payment is a small percentage of the balance, set so that paying only the minimum clears the debt very slowly while interest keeps compounding.

This is why understanding the cost of credit matters: the same purchase can cost very different amounts depending on how it is repaid.

APR: the true cost of credit

The annual percentage rate is a standardised yearly cost of borrowing that includes the effect of compounding and certain charges. It exists so that borrowers can compare products that quote rates differently.

Comparing borrowing options

To choose between borrowing options, put them on the same basis. Convert every rate to an effective annual rate or APR, and consider the total amount repaid over the life of the borrowing, not just the headline rate or the monthly payment. A lower monthly payment over a longer term often costs more in total interest.

Try this

Q1. A £1500\pounds 1500 loan is charged 2%2\% per month and £400\pounds 400 is repaid monthly. Find the balance after one payment. [2 marks]

  • Cue. 1500×1.02−400=1530−400=£11301500 \times 1.02 - 400 = 1530 - 400 = \pounds 1130.

Q2. A credit card charges 1.3%1.3\% per month. Find its effective annual rate. [2 marks]

  • Cue. 1.01312−1=0.16771.013^{12} - 1 = 0.1677, about 16.8%16.8\%.

Q3. Two loans cost the same per month but one runs for 33 years and the other for 55 years. Which is likely to cost more in total, and why? [2 marks]

  • Cue. The 55 year loan, because more payments at the same level mean more total interest paid over a longer term.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA Higher Apps style5 marksA loan of £3000\pounds 3000 is charged 1.2%1.2\% interest per month, and £280\pounds 280 is repaid at the end of each month. Find the balance owing after the first two payments.
Show worked answer →

Each month interest is added then the payment is subtracted. After month one: interest =3000×0.012=£36= 3000 \times 0.012 = \pounds 36, so the balance is 3000+36−280=£27563000 + 36 - 280 = \pounds 2756 (2 marks).

After month two: interest =2756×0.012=£33.07= 2756 \times 0.012 = \pounds 33.07, so the balance is 2756+33.07−280=£2509.072756 + 33.07 - 280 = \pounds 2509.07 (2 marks).

So £2509.07\pounds 2509.07 is still owed after two payments (1 mark). Markers reward applying interest to the current balance each month before subtracting the payment, and working to the nearest penny.

SQA Higher Apps style4 marksTwo credit cards both offer £1000\pounds 1000 of credit. Card A has an APR of 19.9%19.9\%; card B charges 1.4%1.4\% per month. Determine which card is cheaper for borrowing held for a year, supporting your answer with the effective annual rate of card B.
Show worked answer →

Card B's monthly rate compounds, so its effective annual rate is (1+0.014)12−1=1.01412−1=0.1816\left(1 + 0.014\right)^{12} - 1 = 1.014^{12} - 1 = 0.1816, about 18.2%18.2\% (2 marks).

Comparing like with like, card B at 18.2%18.2\% is cheaper than card A at 19.9%19.9\% for borrowing held over a year (1 mark).

APR lets you compare cards on a single annual figure that includes compounding, so card B is the better choice (1 mark). Markers reward computing the effective annual rate from the monthly rate and comparing it against the APR.

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