1. ©G Dear2008 – Not to be sold/Free to use
General Mathematic
(HSC)
Annuities and
Loan Repayments
Annuities
Stage 6 - Year 12
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©G Dear2008 – Not to be sold/Free to use

2. { } (1+r)n-1 A = M r Annuities (1/3)
An Investment with periodical equal contributions.
Interest compounds at the end of each period.
{ }
(1+r)n-1 r
A = M
A is the future value of the investment.
M is the amount of the equal periodical investments.
r is the rate of interest per period as a decimal.
n is the number of periods. 2

3. { } { } { } (1+r)n-1 A = M r Annuities (2/3)
Calculate the value of a $1200 investment, at the end of each year, for 20 years at 4.8% pa compounding annually.
{ }
(1+r)n-1 r
A = M
{ }
( )20- 1
0.048
A = 1200
{ }
( )
0.048
= 1200
= $ 3

4. { } { } { } (1+r)n-1 A = M r Annuities (3/3)
Calculate the value of a $100 investment at the end of each month for 20 years at 4.8% pa compounding monthly.
{ }
(1+r)n-1 r
A = M
Interest
per month
= 4.8% ÷ 12
{ }
( )240- 1
0.004
A = 100
= 0.4%
{ }
= 0.004
( )
0.004
= 100
Periods
= 20y x 12m
= $
= 240
12 monthly installments of $100 produces $ more than 1 annual installment of $1200. 4