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Higher Applications of Mathematics

Repayment schedules

Tracking balances, interest and repayments over time.

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

  • Calculate percentages of changing balances.
  • Subtract money values accurately.
  • Understand opening and closing balances.
  • Read tables row by row.

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 repayment schedule is a table that tracks a loan over time. It shows how much of each payment goes to interest and how much actually reduces the debt.
  • At the start of a loan, interest can take a larger share of the payment. As the balance falls, the interest charge usually falls and more capital is repaid.
  1. Copy the previous closing balance into the next opening balance.
  2. Calculate interest from the opening balance for that row.
  3. Calculate capital repaid as payment minus interest.
  4. Calculate closing balance as opening balance minus capital repaid.
  5. Check that the balance decreases if the payment is larger than the interest.

Key formulae

  • Interest = opening balance x period rate
  • Capital repaid = payment − interest
  • Closing balance = opening balance − capital repaid
  • Next opening balance = previous closing balance

Worked examples

Worked example 1

First two months of a loan schedule

A loan starts at £2,000. Monthly interest is 1%. The payment is £180 per month.

  1. Month 1 interest = 2000 × 0.01 = 20. Capital repaid = 180 − 20 = 160. Closing balance = 2000 − 160 = 1840.
  2. Month 2 interest = 1840 × 0.01 = 18.40. Capital repaid = 180 − 18.40 = 161.60. Closing balance = 1840 − 161.60 = 1678.40.

So: After two payments the balance is £1,678.40.

Worked example 2

Completing a schedule row

A row has opening balance £3,450, monthly interest 0.75%, and payment £220.

  1. Interest = 3450 × 0.0075 = 25.875, so £25.88
  2. Capital repaid = 220 − 25.88 = 194.12
  3. Closing balance = 3450 − 194.12 = 3255.88

Final step: Interest £25.88, capital repaid £194.12, closing balance £3,255.88.

Worked example 3

Three-row schedule

A loan starts at £1,200. Monthly interest is 0.8%. Payments are £160.

  1. Month 1: interest 9.60, capital 150.40, closing 1049.60.
  2. Month 2: interest 8.40, capital 151.60, closing 898.00.
  3. Month 3: interest 7.18, capital 152.82, closing 745.18.

So: After three payments the balance is £745.18.

Worked example 4

Finding a missing payment

Opening balance is £2,800, interest is 1%, and closing balance is £2,610.

  1. Interest = 2800 × 0.01 = 28
  2. Balance after interest = 2828
  3. Payment = 2828 − 2610

Final step: The payment was £218.

Watch out

  • Calculating interest from the original loan each time instead of the opening balance for that row.
  • Calling the whole payment capital repaid.
  • Using closing balance before interest as the next opening balance.
  • Losing pennies by rounding every intermediate value too aggressively.

Spreadsheet connection

Spreadsheet connection

Use columns for opening balance, interest, repayment, capital repaid and closing balance.

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