MATHSLIVE.IE
Need to Know

Financial Maths

The full set of rules, formulas and methods — stripped of worked examples — so you can sit and learn the material.

How to use this. Read each heading. Try to recall the rule in your head before tapping Show me. No score, no pressure — this is where you learn it.

Percentages, Profit & Error

2 cards
Card 1
Percentages — the 5 types

% = out of 100.

Type 1: Find % of a number.

e.g. 6% of €520

Type 2: % increase.

e.g. 9% on €730

Type 3: % given, find number.

e.g. 8% of ? = 654

Type 4: Convert to %.

e.g. 4 as % of 5

Type 5: End value + % change → find original.

e.g. €165 sale, 21% off → original?

Card 2
Profit, margin & error

Profit = selling price − cost price

Mark-up = profitcost price × 100

Margin = profitselling price × 100

% Error = errorreal value × 100

Mark-up uses COST, Margin uses SELLING — don't mix them up!

Ratio, Sig Figs, FX & Tax

4 cards
Card 1
Ratio & proportion

Write in same units.

  • Direct: one up → other up.
  • Indirect: one up → other down (men at work).
Card 2
Significant figures & scientific notation

Significant figures: like decimals, but rest turn to 0's.

Scientific notation: BIG number → positive index.

Card 3
Foreign exchange

Multiply or divide.

Card 4
Tax

Net tax = Gross tax − Tax credit

Compound Interest & Depreciation

2 cards
Card 1
Compound interest

F = P(1 + i)t    P = F(1 + i)t

P = principal,   F = future value.

t = time,   i = rate as a DECIMAL.

Continuous growth: F = Pert

  • r > 0 → growth.
  • r < 0 → decay / depreciation.

APR = borrowing rate.   AER = lending rate.

WATCH: i must be a DECIMAL — 4% is i = 0.04, not 4.
Card 2
Depreciation (decay)

F = P(1 − i)t    P = F(1 − i)t In Tables

Know NEW price → find later: F = P(1 − i)t

Know later price → find NEW: P = F(1 − i)t

Net Book Value (NBV): bring all values to PRESENT and add.

  • NBV > 0 → invest.
  • NBV < 0 → do not invest.

Annuities, Loans & Pensions

3 cards
Card 1
Annuities — timing is everything

APR → monthly: (1 + i)12 = 1 + APR

e.g. 4% APR → monthly i = 1.041/12 − 1

THE BIG QUESTION: when do you spend the money?

Saving (spend in future): series of P values → F.

F = P(1+i) + P(1+i)2 + …

Spend now / won now (payments in future):

P = F(1+i)1 + F(1+i)2 + …

Start of month: first t = 72, n = 72.

End of month: first t = 71, n = 72 (still 72 payments).

Card 2
Loans & mortgages

Amortisation Formula:

A = P · i(1+i)t(1+i)t − 1

  • P = amount borrowed.
  • t = number of instalments.
  • i = interest rate per period.
  • A = monthly instalment.
Card 3
Pensions — pay in, receive out

Concept: Pay In → Pension Pot → Receive Out.

Months from retirement to death:

e.g. (86 − 65) × 12 = 252 months

Part 1 — paying in (present values → future lump):

F = P(1+i)t + P(1+i)t−1 + … + P(1+i)1

Part 2 — pension out (lump → future values):

P = F(1+i)1 + F(1+i)2 + …

Live forever? Use infinite series: S∞ = a1 − r

Bonds & Golden Rules

2 cards
Card 1
Bonds

Two parts — bring BOTH back to present value:

  • A lump sum at maturity.
  • Annuity-style coupon payments.
TIP: Add the present values of both parts to get bond price today.
Card 2
Golden rules
  • i is a DECIMAL (0.04 not 4).
  • Match i to t — monthly i with monthly t.
  • Saving = present values → future.
  • Spending = future values → present.
  • Always identify: P, F, i, t before starting.
  • Read carefully: start vs end of month.