1. General
Maths
FINANCE
in
60
minutes

2. • h7p://www.youtube.com/watch?
v=23zghpS9034

3. Preliminary
Course
1. Earning
Money
2.
Inves1ng
Money
• Wages
• Simple
Interest
• Salaries
• Compound
Interest
• Holiday
loading
• OverOme
and
casual
rates
3. Shares
and
Taxes
• Tax
• Shares
• Budgets
• Income
Tax
• Costs
and
taxes
• Bills

4. HSC
Course
2.
Annui1es
1. Arranging
Credit
• What
are
annuiOes?
• Flat
rate
loan
• Future
value
of
annuiOes
• Hire
purchase
• Present
value
of
annuiOes
• Repayments
Tables
• AnnuiOes
&
loan
• Home
loans/other
costs
repayments
• CalculaOng
repayments
• Repayment
graphs
3. Deprecia1on
• Straight
line
method
• Declining
balance
method

5. Earning
• A
salary
is
a
fixed
payment
for
a
certain
period
of
Ome,
usually
a
year
• A
wage
is
usually
paid
at
a
set
rate
per
hour
• Over1me
and
other
penalty
rates
are
usually
paid
at
some
mulOple
of
hourly
rate
eg
double
Ome
means
double
the
hourly
rate.
• Gross
pay
is
the
total
of
all
pay
received
before
any
deducOons
have
been
made
• Net
pay
=
gross
pay
–
deducOons
(deducOons
include
superannuaOon,
tax,
union
fees
etc)

6. Earning
Ques4ons
Angus
receives
a
gross
pay
of
$630
for
a
37½
hour
week.
(a)
Find
Angus’
hourly
rate
of
pay.
(b)
If
Angus’
weekly
gross
pay
was
$756
and
all
overOme
was
paid
at
Ome-­‐and-­‐a
half,
how
many
hours
overOme
did
Angus
work?

7. Inves4ng
• Simple
Interest
is
paid
just
on
the
Principal
(or
the
original
sum
of
money)
• Compound
interest
is
paid
on
the
principal
and
on
interest
already
earned
• Interest
rates
are
usually
given
as
percentages
–
you
should
convert
to
decimals.
eg
76%
=
0.76
• p.a.
Means
per
annum
or
per
year
• To
find
the
monthly
rate
–
divide
yearly
rate
by
12

8. Inves4ng
Money
Ques4ons
1. The
Advantage
Bank
offers
investors
15%
p.a.
simple
interest.
Express
this
interest
as
a
(i)
monthly
rate
(ii)
quarterly
rate
2.
Grant
won
$42000
on
lo7o.
He
invested
it
in
a
Credit
Union
account
for
18
months
at
5%
p.a.
How
much
will
his
investment
be
worth
aker
18
months?

9. Inves4ng
Money
Ques4ons
3.
Lisa
invests
$5000
in
a
term
deposit
which
pays
8%
p.a.
compounding
quarterly.
The
term
of
her
investment
was
1
year.
How
much
will
she
receive,
including
interest,
when
her
investment
matures
at
the
end
of
the
year?

10. Inves4ng
Money
Ques4ons
4.
James
is
going
to
invest
$15000
at
8%
p.a.
compounded
monthly.
How
long
will
he
need
to
invest
the
money
to
have
$30000
in
the
bank?

11. Shares
and
Taxes
• Shares
are
part-­‐ownership
of
a
company.
They
enOtle
the
owner
to
a
share
in
the
profits
in
the
company.
Payments
made
to
shareholders
are
called
dividends.
Dividend
yield
is
a
measure
of
the
return
to
shareholders.
Dividend
yield
=
annual
dividend
share
x
100%
market
price
per
share

12. Shares
and
Taxes
• Taxable
income
=
income
that
remains
aker
all
allowable
deducOons
have
been
taken
out
from
gross
income.
• Tax
tables
are
used
to
calculate
tax
payable
• Tax
payable
>
tax
already
paid

pay
more
tax
• Tax
already
paid
>
tax
payable

refund

13. Shares
and
Taxes
Exercises
Jay
has
received
his
group
cerOficate.
It
shows
his
gross
income
to
be
$48
843
and
the
amount
of
tax
deducted
to
be
$12
153.
(a) Jay’s
allowable
deducOons
total
$569.
What
is
his
taxable
income?
(b)
If
a
taxable
income
between
$20001
and
$50000
pays
$2380
+
30
c
for
every
dollar
over
$20000,
find
the
tax
payable.
(c) Calculate
the
amount
of
his
medicare
levy
at
a
rate
of
1.5%
of
taxable
income.
(d) Will
Jay
have
to
pay
more
tax
or
will
he
receive
a
refund?
JusOfy
your
answer.

14. Shares
and
Taxes
Ques4ons
Jan
buys
3000
shares
in
a
company
at
a
price
of
$4.60
per
share.
(a)
If
brokerage
costs
are
2.5%
and
stamp
duty
15%,
find
the
total
cost
of
the
shares.
(b) The
dividend
yield
is
4.8%
when
the
market
price
is
$4.75.
Find
the
total
dividends
paid
to
Jan.
(c) Aker
the
dividends
have
been
paid,
Jan
sells
the
shares.
She
receives
$4.95
per
share
aker
costs.
Find
Jan’s
profit
or
loss
from
owning
these
shares.

15. Arranging
Credit
• flat-­‐rate
loan
–
interest
charged
on
iniOal
amount
borrowed
• Principal
=
amount
borrowed
• Term
=
Ome
over
which
loan
is
repaid
• Total
to
repay
=
principal
+
interest
• Repayment
amount
=
total
to
repay
number
of
repayments
• Interest
=
total
to
be
repaid
-­‐
principal

16. Arranging
Credit
• Reducing
balance
loan
–
interest
charged
on
amount
owing.
Amount
owing
aker
1
period
=
P
+
I
–
Repayment
(This
amount
becomes
the
new
principal)
• Credit
cards
–
some
offer
an
interest
free
period
so
no
interest
charged
as
long
as
account
paid
by
due
date
• Credit
cards
generally
charge
daily
interest
–
divide
annual
interest
by
365.
Take
care
–
because
percentages
are
small
it
is
easy
to
think
they
are
already
decimals.

17. Arranging
Credit
Exercises
1. Holly
borrows
$1800
and
repays
$90
a
month
for
2
years.
(a)
How
much
in
total
does
Holly
repay?
(b)
How
much
interest
does
Holly
pay?
(c)
What
flat
rate
of
interest
has
Holly
been
paid?

18. Arranging
Credit
Exercises
2. Maddi
used
a
loan
calculator
on
an
internet
site
to
draw
up
a
table
of
the
monthly
repayments
if
she
borrows
$70000
at
7.8%
fixed
interest.
Loan
period
5
10
15
20
25
30
in
years
Monthly
$1412.66
$841.91
$660.90
$576.83
$531.03
$503.91
repayments
(a) What
total
amount
must
be
repaid
if
the
loan
is
taken
over
15
years?
(b) How
much
more
is
paid
if
the
loan
is
taken
out
over
30
years
rather
than
15?

19. Annui4es
• An
annuity
is
a
type
of
investment
where
equal
amounts
of
money
are
invested
at
regular
intervals
(periods)
and
interest
is
compounded
at
the
end
of
every
period.
• ContribuOon
=
amount
of
money
invested
every
per
period
period
• Future
value
=
total
value
at
end
of
investment
period
• Present
value
of
an
annuity
=
money
to
be
invested
now
to
accumulate
to
the
future
or
final
value
of
the
annuity
• Calculator
–
check
your
entries
as
really
easy
to
make
mistakes.
Try
to
esOmate
answer
as
another
check.

20. Annui4es
Formulae
• Work
out
what
informaOon
you
have
been
given
in
the
quesOon
• Make
a
list
of
this
informaOon
• Decide
which
formula
to
use
-­‐
which
one
connects
all
this
informaOon
together??
• SubsOtute
the
data
into
the
formula
• Calculate
–
take
one
last
look
at
the
display
-­‐
be
careful
to
check
you
have
entered
everything
correctly
before
you
press
equals

21. Annui4es
Formulae
⎧ (1 + r) − 1 ⎫ n
A=M⎨ ⎬
⎩ r ⎭
A
=
Future
value
or
Amount
required
in
the
future
M
=
payment
per
period
r
=
percentage
rate
of
interest
(as
a
decimal)
n
=
number
of
compounding
periods
Find
the
value
at
the
end
of
7
years
of
an
annuity
of
$125
paid
at
the
end
of
each
month,
interest
compounding
monthly
at
0.5%
per
month.

22. Annui4es
Formulae
A
N=
(1 + r) n
What
sum
of
money
invested
now
(interest
compounded
monthly
at
0.375%
per
month)
would
give
$7500
at
the
end
of
4
years?

23. Annui4es
Formulae
⎧ (1 + r)n − 1 ⎫
N=M⎨ n ⎬
⎩ r(1 + r) ⎭
What
sum
of
money
invested
for
10
years
now
(interest
at
0.625%
per
month,
compounded
monthly)
would
be
equivalent
to
$525
invested
at
the
end
of
each
month
at
the
same
rate
of
interest?

24. Annui4es
Formulae
⎧ (1 + r)n − 1 ⎫
N=M⎨ n ⎬
⎩ r(1 + r) ⎭
This
1me
we
are
finding
M
What
amount
would
need
to
be
invested
each
month
for
15
years
to
be
equivalent
to
an
amount
of
$60000
invested
now?
Interest
is
compounded
monthly
at
0.75%
per
month.

25. Deprecia4on
• An
asset
is
something
of
value
• Many
assets
decrease
in
value
over
Ome
–
called
depreciaOon.
• Salvage
value
=
current
value
of
asset
S = V0 (1− r )
n
Note
that
someOmes
things
appreciate
–
S
=
Salvage
value
increase
in
value
eg
Vo
=
IniOal
value
houses
–
same
r
=
interest
rate
per
period
as
a
decimal
formula,
sub
in
+
n
=
number
of
periods
sign
in
bracket

26. Deprecia4on
There
are
2
methods
for
calculaOng
depreciaOon
• Straight
line
deprecia1on
–
asset
depreciates
by
the
same
amount
each
period.
Graph
is
a
straight
line.
• Declining
balance
deprecia1on
–
value
decreases
by
a
fixed
percentage
each
period.
Graph
is
a
curve.

27. Deprecia4on
Exercises
• On
1
July
2003
Lee
bought
a
truck
for
$73000.
On
1
July
2010
the
truck
was
valued
at
$36600.
The
straight
line
method
of
depreciaOon
was
used.
(a) What
is
the
amount
of
depreciaOon
per
year?
(b) What
will
the
truck
be
worth
on
1
July
2013?
(c) In
which
year
will
the
last
amount
of
depreciaOon
be
allowed?
(d) If
the
declining
balance
method
of
depreciaOon
had
been
used
instead,
what
rate
of
depreciaOon
would
give
the
same
value
of
the
truck
in
2010?

28. Past
HSC
QuesOons

29. Past
HSC
QuesOons

30. Past
HSC
QuesOons

31. Past
HSC
QuesOons