Summary Finance, Growth and Decay - Mathematics Grade 12 (IEB)

Financial mathematics
Interest

Simple interest Compound interest
A = P(1 + i x n) A = P(1 + i)n
A – final amount A – final amount
P – initial amount P – initial amount
i – interest rate i – interest rate
n – time period n – time period
Arithmetic sequence Geometric sequence
Linear graph Exponential graph


Depreciation

Simple depreciation
(simple decay or straight line or flat rate)
A = P(1 - i x n)
A – final amount
P – initial amount
i – interest rate
n – time period

Arithmetic sequence
Linear graph



Compound interest
(compound decay or deducing balance)
A = P(1 - i)n
A – final amount
P – initial amount
i – interest rate
n – time period

Geometric sequence
Exponential graph

, Compounding interest
Compounding periods
- Yearly (1 payment per year)
- Semi-annually (2 payments per year)
- Quarterly (4 payments per year)
- Monthly (12 payments per year)
- Weekly (52 payments per year)
- Daily (365 payments per year)
𝑖 (𝑚)
A=P(1+ 𝑚
)m x n

Nominal interest: the rate quoted by the bank (i(m))

Effective interest: the actual amount received (ie)
𝑖 (𝑚) m
1 + ie = (1 + 𝑚
)
(n becomes 1 as we are comparing)


Changing Formulas
Simple:
A = P (1 + i.n)

P = A(1 + i.n)-1
𝐴−𝑃
i=
𝑃𝑛
𝐴−𝑃
n= 𝑃𝑖

Compound:
A = P (1 + i)n

P = A (1 + i)-n
𝐴
i = n√(𝑃) – 1
𝐴
n = log(1+i)
𝑃