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Higher Applications of Mathematics

Finance formula reference

A compact reference for the Finance formulae and methods used across Higher Applications of Mathematics.

Simple interest

I = Prt

Symbols

  • I = interest
  • P = original amount
  • r = rate as a decimal
  • t = time in years

Use when

Use when interest is calculated on the original amount only.

Quick example

£800 at 5% for 3 years gives I = 800 × 0.05 × 3 = £120

Compound interest

A = P(1 + r)n

Symbols

  • A = final amount
  • P = starting amount
  • r = rate per period
  • n = number of periods

Use when

Use when the amount increases by a percentage repeatedly.

Quick example

£1,000 at 4% for 2 years gives A = 1000(1.04)² = £1,081.60

Effective annual rate

EAR = (1 + monthly rate)12 − 1

Symbols

  • monthly rate = monthly percentage as a decimal
  • EAR = true yearly rate after compounding

Use when

Use when a monthly interest rate is compounded over a full year.

Quick example

1% per month gives EAR = 1.0112 − 1 = 12.68%

Present value

PV = FV / (1 + r)n

Symbols

  • PV = value today
  • FV = future value
  • r = discount rate
  • n = number of periods

Use when

Use when finding what future money is worth today.

Quick example

£5,000 in 4 years at 3% has PV = 5000 / 1.03⁴ = £4,442.44

Future value

FV = PV(1 + r)n

Symbols

  • FV = future value
  • PV = value today
  • r = growth rate
  • n = number of periods

Use when

Use when finding what today's money will be worth later.

Quick example

£2,500 at 3% for 5 years gives FV = 2500(1.03)⁵ = £2,898.19

Percentage change

percentage change = change / original x 100%

Symbols

  • change = new value − original value
  • original = starting value

Use when

Use when comparing an increase or decrease with the starting value.

Quick example

£80 rising to £92 is 12 / 80 × 100 = 15%

Inflation / real value

real value = cash value / (1 + inflation rate)n

Symbols

  • cash value = future amount
  • inflation rate = decimal rate
  • n = years

Use when

Use when finding today's purchasing power of future money.

Quick example

£10,000 in 6 years at 2.5% has real value £10,000 / 1.025⁶ = £8,623.00

Repayment schedule columns

interest = opening balance x rate; capital repaid = payment − interest; closing balance = opening balance − capital repaid

Symbols

  • opening balance = balance at start of row
  • payment = amount paid that period
  • closing balance = next row's opening balance

Use when

Use when tracking a loan or credit agreement row by row.

Quick example

Opening £1,000, interest £12, payment £100 gives capital £88 and closing £912.

Expected value

expected value = probability x value

Symbols

  • probability = chance as a decimal
  • value = claim, payout or cost

Use when

Use when comparing insurance risk or long-run average cost.

Quick example

8% chance of a £500 claim gives 0.08 × 500 = £40

Net pay

net pay = gross pay − deductions

Symbols

  • gross pay = pay before deductions
  • deductions = tax, National Insurance, pension and similar amounts

Use when

Use when finding take-home pay.

Quick example

Gross £2,700 with £610 deductions gives net pay £2,090.

Budget surplus / deficit

surplus or deficit = income − spending

Symbols

  • positive answer = surplus
  • negative answer = deficit

Use when

Use when checking whether a budget balances.

Quick example

Income £2,200 and spending £2,340 gives −£140, a £140 deficit.