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