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Higher Applications of Mathematics

Interest rates

Simple and compound interest in practical contexts.

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 percentages to decimals and decimals to percentages.
  • Use powers on a calculator accurately.
  • Round money to the nearest penny at the final answer.
  • Recognise whether a rate is annual, monthly, fixed or variable.

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

  • Interest is the charge for borrowing money or the reward for saving money. In Higher Applications, the important decision is not only which formula to use, but what the rate and time period actually mean.
  • Simple interest is calculated on the original amount only. Compound interest is recalculated after each interest period, so interest can earn further interest. Rates may be fixed, variable, annual, monthly, or quoted as an effective annual rate.
  1. Identify the original amount, the rate, and the time period.
  2. Check whether the question describes simple interest or compound interest.
  3. Make the rate and time match. For monthly compounding, use a monthly rate and number of months.
  4. For effective annual rate, compound the monthly rate over 12 months.
  5. Round at the end and write a sentence explaining the financial meaning.

Key formulae

  • Simple interest: I = Prt, where r is a decimal and t is in years
  • Compound value: A = P(1 + r)n
  • Monthly rate from nominal annual rate: monthly rate = annual rate / 12
  • Effective annual rate from monthly rate: EAR = (1 + monthly rate)12 − 1

Worked examples

Worked example 1

Compound interest on savings

A pupil saves £2,400 in a fixed-rate account paying 4.2% per year for 3 years.

  1. Use A = P(1 + r)n with P = 2400, r = 0.042, n = 3.
  2. A = 2400(1.042)³.
  3. A = 2400 × 1.131409288 = 2715.382291.
  4. Round money to the nearest penny.

So: The account is worth £2,715.38. The interest earned is £315.38.

Worked example 2

Effective annual rate from a monthly rate

A credit card charges 1.55% interest per month. Find the effective annual rate.

  1. Convert the monthly rate to a decimal: 1.55% = 0.0155
  2. Use EAR = (1 + 0.0155)12 − 1.
  3. EAR = 1.015512 − 1 = 0.2029..
  4. Convert to a percentage.

Final step: The effective annual rate is about 20.3%. This is higher than 1.55% x 12 because of compounding.

Worked example 3

Comparing fixed and variable rates

A saver invests £3,200. Account A pays a fixed 4.1% for two years. Account B pays 3.6% in year 1 and 4.8% in year 2.

  1. Account A: A = 3200(1.041)² = 3467.6832
  2. Account B: A = 3200(1.036)(1.048) = 3475.0464
  3. Compare the final balances.

So: Account B gives £3,475.05, which is £7.37 more than Account A.

Worked example 4

Monthly compounding on a savings account

A cash ISA has £5,000 invested at a nominal annual rate of 3.6%, compounded monthly, for 18 months.

  1. Monthly rate = 3.6% / 12 = 0.3% = 0.003
  2. There are 18 monthly compounding periods.
  3. A = 5000(1.003)18 = 5277.0069.

Final step: The balance is £5,277.01.

Watch out

  • Using 4.2 instead of 0.042 in a formula.
  • Treating a monthly rate as if it is an annual rate.
  • Using simple interest when the balance compounds each period.
  • Rounding too early in a multi-step calculation.

Spreadsheet connection

Spreadsheet connection

Model repeated percentage change, compare fixed and variable rates, and calculate effective annual rate.

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