Back to Finance

Higher Applications of Mathematics

Loans and credit cards

Borrowing, repayments, interest and financial choices.

Formula referenceFinance mixed quiz

Formula reference

Check the key Finance formulae and when to use each one.

Mixed revision quiz

Review the whole Finance section with adaptive feedback.

Before you start

  • Convert annual rates to monthly rates when needed.
  • Calculate a percentage of a balance.
  • Understand that repayments reduce outstanding balance, not the original loan.
  • Keep track of the order: interest then payment unless told otherwise.

Method chooser

Which method do I use?

Are you finding interest on the original amount only?

Use simple interest.

Is the amount increasing by a percentage repeatedly?

Use compound interest.

Are you finding what future money is worth today?

Use present value.

Are you finding what today's money will be worth later?

Use future value.

Are there regular payments, deposits or withdrawals?

Use a payment timeline.

Are you tracking a loan balance after repayments?

Use a repayment schedule.

Are you comparing insurance policies or risk?

Use expected value and excess comparisons.

Are you working with gross pay, deductions and take-home pay?

Use net pay.

Are you comparing prices over time with inflation?

Use inflation / real value.

Finance lesson

Key idea

  • A loan balance increases when interest is added and decreases when repayments are made. Credit cards work in a similar way, but the interest rate is often monthly and minimum payments can make the debt last much longer.
  • The total cost of credit is the total amount repaid minus the original amount borrowed. This is often more useful than only comparing monthly payments.
  1. Start with the opening balance.
  2. Calculate interest for the period using the current balance.
  3. Add any interest or fees.
  4. Subtract the repayment or minimum payment.
  5. Use the closing balance to discuss total cost and whether the debt is reducing quickly.

Key formulae

  • Interest for a period = outstanding balance x period rate
  • New balance = outstanding balance + interest − payment
  • Total cost of credit = total paid − amount borrowed
  • Monthly rate from annual nominal rate = annual rate / 12

Worked examples

Worked example 1

Loan balance after one payment

A £6,000 loan is charged 7.2% per year, applied monthly. The borrower pays £190 at the end of the first month.

  1. Monthly rate = 7.2% / 12 = 0.6% = 0.006
  2. Interest = 6000 × 0.006 = 36
  3. Balance after interest = 6036
  4. Closing balance = 6036 − 190 = 5846

So: The balance after the first payment is £5,846.00.

Worked example 2

Credit card minimum payment

A credit card balance is £1,250. Monthly interest is 1.7%. The minimum payment is 3% of the balance after interest.

  1. Interest = 1250 × 0.017 = 21.25
  2. Balance after interest = 1271.25
  3. Minimum payment = 0.03 × 1271.25 = 38.1375
  4. Closing balance = 1271.25 − 38.14 = 1233.11

Final step: The minimum payment is £38.14 and the closing balance is £1,233.11.

Worked example 3

Total cost of a personal loan

A borrower takes a £9,000 loan and repays £287 per month for 36 months.

  1. Total repaid = 287 × 36 = 10332
  2. Total cost of credit = total repaid − amount borrowed
  3. Cost = 10332 − 9000 = 1332

So: The total cost of credit is £1,332.

Worked example 4

Credit card payment after a purchase

A credit card balance is £640. A purchase of £210 is added, then monthly interest of 1.8% is charged. A payment of £90 is then made.

  1. Balance after purchase = 640 + 210 = 850
  2. Interest = 850 × 0.018 = 15.30
  3. Balance after interest and payment = 850 + 15.30 − 90

Final step: The closing balance is £775.30.

Watch out

  • Using the annual rate directly as a monthly rate.
  • Subtracting the repayment before adding interest when the agreement says interest is added first.
  • Comparing loans only by monthly payment and ignoring length of loan.
  • Forgetting that a minimum credit card payment may barely reduce the balance.

Spreadsheet connection

Spreadsheet connection

Track balances, interest charges, repayments and minimum payment models.

Open spreadsheet skill

Next step

Move into practice

Use the method notes to choose the correct financial model, then try varied rates, time periods, tables and decision contexts.

Finance mixed quiz