FINANCIAL MATHEMATICS

REVISION – GRADE 10

APPRECIATION / GROWTH (Gains value)

𝑨 = 𝑷(𝟏+ 𝒊 .𝒏) 𝑨 = 𝑷(𝟏 + 𝒊)𝒏

SIMPLE interest COMPOUND interest

Where………

𝑨 = final/accumulated amount

𝑷 = starting/original amount

𝒏 = number of years

𝒊 = interest rate 𝑟

100

Interest calculated on only

the initial amount

Interest calculated on the initial

amount AND any subsequent

interest that is earned

Used in……..

Used in……..

HIRE PURCHASE LOANS

Short-term loans to buy goods

on credit, normally repaid in

equal monthly instalments

INFLATION

The rising cost of goods and

services

POPULATION GROWTH

TIMELINES

Can be used to VISUALLY represent more complicated situations in Financial Maths, like….

1. Money going in and out of an account

2. Change of interest rates during a period of time

3. Both money going in and out of an account and the interest rate changing

IMPORTANT

‼

Round off in the FINAL answer only

When working with money we round off to

2 (two) decimal places

GRADE 11

DEPRECIATION / DECAY (Loss of value)

𝑨 = 𝑷(𝟏− 𝒊 .𝒏) 𝑨 = 𝑷(𝟏 − 𝒊)𝒏

LINEAR (simple) depreciation COMPOUND depreciation

Where………

A = book or scrap value

P = present value

i = depreciation rate 𝑟

100

n = time period

Also known as simple decay or

straight line depreciation

Also known as depreciation on a

reducing balance

Graphical representation……..

Graphical representation…..

NOMINAL VS EFFECTIVE INTEREST RATES

(COMPOUND INTEREST)

Annual effective rate is equivalent to the nominal rate per annum compounded

monthly, because it produces the same accumulated amount.

Nominal interest rate = the quoted interest rate per compounding period (m)

Effective interest rate = the equivalent actual (working) interest rate per annum

Study the formula: 𝒊𝒆𝒇𝒇 = 𝟏+𝒊𝒏𝒐𝒎

𝒎 𝒎

− 𝟏 (it is not on the formula sheet)

𝒊𝒆𝒇𝒇 = effective rate (annual)

𝒊𝒏𝒐𝒎 = nominal rate

m = number of compoundings per year

Terminology

Changing interest rates & time periods

Yearly → n & i don’t change Half yearly → 𝑛 × 2 & 𝑖 ÷ 2 Quarterly → 𝑛 × 4 & 𝑖 ÷ 4 Monthly → 𝑛 × 12 & 𝑖 ÷ 12 Weekly → 𝑛 × 52 & 𝑖 ÷ 52 Daily → 𝑛 × 365 & 𝑖 ÷ 365