Transcript Interest Slideshow C13

FINANCIAL MATHEMATICS
Today’s Topics:
⊲Simple Interest
⊲Compound Interest
⊲Rule 72
⊲Fixed Term Deposits
Simple
Versus
Compound
A Review of Simple Interest
SIMPLE INTEREST Is:
 Simple (to compute)
 Interest paid only on the
original principal, C,
 Also referred to as flat
rate interest

Use the following
simple interest
formula:
I=C×r×n
where C is the principal or
money deposited, r is the
simple interest per annum as
a decimal, n is time
expressed in terms of years
A Review of Compound Interest
 Compound interest is the
interest earned not only on
the original principal, but
also on all interests earned
previously.
In other words, at the end
of each year, the interest
earned is added to the
original amount and the
money is reinvested.
 A = C x (1 + r/100)n
 I = C x (1 + r/100)n - C
 This means that the
interest is added to the
principal each period so
that the principal
continues to grow
throughout the life of the
loan or investment.
 Remember, to find total
interest earned from the
beginning of the loan or
investment to the end,
subtract the principal from
the final balance
Compound
Interest
Formulas
•A = C x (1 + r/100)n
•I = C x (1 + r/100)n - C
A = Future Value or Final Balance
C = Present Value or Principal
R = Interest rate per compound period
N = the number of periods compounded
Compounding interest is "interest on interest." It
is a method of calculating interest where the
interest is added to the original principal. This
new value is now our principal for the next time
period. In this method the interest earned in past
terms can earn interest in future terms. Simple
interest is a type of interest that is paid only on
the original amount deposited and not on past
interest paid.
Let’s Use the Equation Solver Feature of the
Graphing Calculator to Compute Simple Interest
Prepare to write the keystrokes for computing simple
interest into your notes.
Solve the Interest Formula: I = C x R x N for zero like so:
Zero = (C x R x N) – I
Place this expression in the equation editor.
(NOTE: preferably use y8 – y0)
Keystrokes Cont’d: Math, ↑ENT (or 0) , VARS, YVARS, ENT, FC#
You will see the variable prompts. Fill in all variables provided in
the problem and solve for the one missing by going to the
entry and pressing “Alpha, Solve”/ “Alpha, ENT”
Use the Equation Solver Feature of the GDC to
Compute Periodic Repayments Too!
Write the keystrokes for calculating periodic repayments in your notes
Solve the Repayment Formula: Rp = (C + I)/N for zero
i.e. Repayment = (Principal + Interest)/# of Repayments
Zero = (C + I)/N – Rp
Place this expression in the equation editor.
(NOTE: preferably use y8 – y0)
Remaining Keystrokes: Math, ↑ENT (or 0), VARS, YVARS, ENT, FC#
You will see the variable prompts. Fill in all variables provided in
the problem and solve for the one missing by going to the
entry and pressing “Alpha, Solve”/ “Alpha, ENT”
Let’s Practice Solving Simple Interest
Problems using the equation Solver:
 Turn in your books to page 427.
Work Ex 9 to practice the keystrokes you just learned.
Also, Work Ex 13 on pages 429-430.
 Meanwhile, I will prepare ELMO for your viewing so
that we can verify calculator keystrokes and practice
problems together.
the graphing calculator can also
solve compound interest
 First, since this unit is dealing with financial math, set
your decimal to float 2 places
Keystrokes: Mode, float, 2
Next, choose APPS, 1 – Finance, 1 – TVM Solver
Your screen should look like this!!!
Financial Math: TVM Solver
 N = 0.00
See Investigation 1 for meanings: p434
 I% = 0.00
N (number of payments/time periods)
I% (interest rate)
PV (present value of the investment)
FV (future value of the investment)
P/Y (number of payments per year)
C/Y (number of compounding periods
 PV = 0.00
 PMT = 0.00
 FV = 0.00
 P/Y = 1.00
 C/Y = 1.00
 PMT: END
per year)
BEGIN
FYI
TVM Solver - Time Value of Money Manager(TVM)
Use time-value-of-money (TVM) functions (menu items 2
through 6) to analyze financial instruments such as
annuities, loans, mortgages, leases, and savings
Each TVM function takes zero to six arguments,
which must be real numbers. The values that you
specify as arguments for TVM functions are not stored
to the TVM variables
Note: To store a value to a TVM variable, use the TVM
Solver or use STO and any TVM variable on the
FINANCE VARS menu.
FINANCIAL CALCULATIONS
To display the FINANCE CALC menu, press APPS, ENT. CALC VARS
1: TVM Solver... : Displays the TVM Solver.
2: tvm_Pmt : Computes the amount of each
payment.
3: tvm_I%: Computes the interest rate per year.
4: tvm_PV: Computes the present value.
5: tvm_N: Computes the number of payment
periods.
6: tvm_FV: Computes the future value.
7: npv(: Computes the net present value.
The Previous slide shows the meanings of
the abbreviations used
in Financial
Calculations and Financial Math. To use
that feature, we must place all given
variables in parenthesis. The missing
variable is automatically solved for if this
method is used.
We will practice using the TVM Solver
Only!!! For an example on how to compute
compound interest variables using the
TVM solver, see the next slide.
Let’s Practice Using the TMV Solver
 Go to page 431 of your
 Keystrokes:
textbook.
 It reads:
Calculate the interest paid
on a deposit of $6000 at
8% p.a. (per annum)
compounded annually
for 3 years.
Float: 2, APPS, ENT, ENT
N= 36 payments (3 years)
I%= 8.00
PV = -6000.00
PMT=0.00
FV = ?
P/Y = 12 (1 year)
C/Y = 12 (1 year)
Here’s a You Tube Video!!!
Watch This -
Follow along
with the video
for extra
practice using
the TVM
Solver
Click on the Link Below
http://www.youtube.com/wa
tch?v=Ku4VPMSP2xM&feat
ure=related
Other Concepts To Know…
Fixed Term Deposits
Effective/Effective Rate
 These deposits are ‘locked
 Typical Question:
away’ by a financial
institution for a fixed time
period of one month to ten
years at a FIXED rate.
Interest is accrued or
compounded, therefore the
principal or deposit increases
during the fixed term. The
longer the money is locked
away the better!
Find the effective after tax
return if the investor’s tax
rate is 48.5 cents in the dollar
(i.e. 48.5%)
Turned to p.441
The effective rate is the interest
rate compounded annually.
R = (1 + i)c - 1
Last Concept – Rule of 72
 The rule of 72 is used to figure out when your money
will double. If you divide 72 by the interest rate you are
earning (or paying) the answer will give you the
number of years until your money doubles. This rule
only works on interest that is compounded once a year.
See IVG 1 – How Long Will It Take To Double My $?
Let’s Try to Watch this You Tube Video  http://www.youtube.com/watch?v=Ldvvgvst75w
ASSIGNMENT: Group Work - (See Syllabus)
TOPIC FOR NEXT CLASS: Foreign Exchange
QUESTION TO PONDER:
Is the USD weak
or strong?
THE END