Download on interest - Wythe County Schools Moodle Site

2.4.2.G1
Time Value of Money Math
Advanced Level
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 1
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Simple Interest vs.
Compound Interest
2.4.2.G1
Simple Interest
Compound Interest
Interest earned on the
principal investment
only
Earning interest on the
principal and on
previous interest earned
Example: You deposit $200
in a 18-month CD and let
the money earn interest
Example: you deposit $200 in
a money market account that
compounds interest quarterly
Principal is the original amount of
money invested or saved
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 2
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Simple Interest Equation: Step 1
Prt = I
P
Principal
r
t
Interest
Rate
Time
Period
I
Interest
Earned
$1,000 invested at 7% interest rate for 5 years
1,000
.07
5
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 3
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
350.00
2.4.2.G1
Simple Interest Equation: Step 2
P+I =FV
P
Principal
I
FV
Interest
Earned
Future
Value of
Investment
$1,000 invested at 7% interest rate for 5 years
1,000
350
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 4
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
$1,350
2.4.2.G1
Compound Interest Equations
There are two methods for calculating
compound interest
Single deposit
investment
Periodic investments
A single sum of money
invested once at the
beginning of the investment
period
Equal amounts of money are
invested at regular intervals,
such as yearly, monthly, or
biweekly
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 5
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Compound Interest Equation –
Single Deposit Investment
FV = future value of investment
P = principal or original balance
r = interest rate expressed as a
decimal
n = number of times interest is
compounded annually
t = number of years
$1,000 invested at 7% interest rate
compounded annually for 5 years
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 6
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Compound Interest Equation –
Periodic Investments of Equal Amounts
FV = future value of investment
P = periodic deposit amount
r = interest rate expressed as a
decimal
n = number of times interest is
compounded annually
t = number of years
$1,000 invested every year at 7% annual
interest rate for 5 years
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 7
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Comparing Simple versus
Compound Interest
Simple Interest =
$1,350.00
Compound Interest
for a Single Deposit
Investment = $1,402.55
Why are they different?
By reinvesting the interest earned,
the interest payment keeps growing
as interest is compounded on
interest
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 8
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Comparing Compound Interest
on a Single Deposit versus
Periodic Investments
Compound Interest
on a Single Deposit =
$1,403.00
2.4.2.G1
Periodic Investments of
Equal Amounts =
$5,750.74
To make the most of your money,
utilize compound interest and
continue to invest!
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 9
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Compound Interest
• Number of times interest is compounded
has effect on return
• Compounding more frequently equals
higher returns
$1,000 invested at 7% for 5 years
Compounding
Method
Compounded
how often?
Amount
Investment is
Worth
Daily
Monthly
Quarterly
Semi-annually
Annually
365
12
4
2
1
$1,419.02
$1,417.63
$1,414.78
$1,410.60
$1,402.55
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 10
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Let’s Compare:
Compound Interest Equation –
Single Deposit Investment
2.4.2.G1
$1,000 invested at
7% interest rate
compounded
annually for 5 years
$1,000 invested at
7% interest rate
compounded
quarterly for 5 years
Earned $12.23 more because the interest
was compounded more frequently
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 11
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Let’s Compare:
Compound Interest Equation –
Periodic Investments
2.4.2.G1
$1,000 invested
every year at 7%
annual interest rate
for 5 years
$1,000 invested
quarterly at 7%
annual interest rate
for 5 years
Earned $17,950.87 more because you contributed
to the account quarterly and the interest was
compounded more frequently
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 12
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Smart Investing
Every variable
in the formula
impacts the
amount of
your return
Rule of Thumb:
The higher the
variable, the
greater your
return
P = Principal
The larger the principal investment,
the greater your return
R = Interest Rate
The higher the interest rate, the
greater your return
N = # of Times Interest is
Compounded per Year
The more often the interest is
compounded, the greater your
return.
T = Number of Years
The longer you leave your money in
the investment, the greater your
return
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 13
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Smart Investing
Which would you choose?
An investment
earning
compound
interest
OR
An investment
earning
simple
interest
Largest
return
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 14
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Smart Investing
Which would you choose?
An investment
earning an
interest rate
of 2%
OR
An investment
earning an
interest rate
of 2.1%
Largest
return
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 15
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Smart Investing
Which would you choose?
An investment
with an
interest rate
compounded
monthly
OR
An investment
with an
interest rate
compounded
yearly
Largest
return
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 16
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice Activities
Choose your practice method
Practice calculating
using the step-by-step
method
(basic calculator)
Practice calculating by
entering all variables
into the formula
(advanced calculator)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 17
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Practice calculating using
the step-by-step method
(basic calculator)
Use with Time Value of Money Math
Practice – Basic Calculator Worksheet
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 18
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #1
Camila deposited $600.00 into a savings account one
year ago. She has been earning 1.2% in annual simple
interest. Complete the following calculations to
determine how much Camila’s money is now worth.
P
600.00
P
600.00
Step One:
T
R
.012
1
Step Two:
I
7.20
I
7.20
A
607.20
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 19
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #1
How much is Camila’s investment
worth after one year?
$607.20
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 20
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #2
Felipe’s grandparents have given him $1500.00 to
invest while he is in college to begin his
retirement fund. He will earn 2.3% interest,
compounded annually. What will his investment
be worth at the end of four years?
What is the equation?
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 21
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #2
Step One: Divide nr
.023
1
.023
Step Three: Multiply
by exponent
1.023
4
1.095
Step Two: Add 1
1
.023
1.023
Step Four: Multiply by
principal
1.095
1500
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 22
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
1642.83
2.4.2.G1
Time Value of Money Math
Practice #2
What will Felipe’s investment be worth at the end
of four years?
$1642.83
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 23
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #3
Nicole put $2000.00 into an account that pays 2%
interest and compounds annually. She invests
$2000.00 every year for five years. What will her
investment be worth after five years?
What is the equation?
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 24
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Time Value of Money Math
Practice #3
Step One: Divide nr
.02
1
.02
1
Step Three: Multiply
by exponent
1.02
(1x5)
Step Two: Add 1
1.104
2,000
1.02
Step Four: Subtract 1
1.104
Step Five: Multiply by principal
1.104
.02
208.16
1
.104
Step Six: Divide by rn
208.16
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 25
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
.02
2.4.2.G1
2.4.2.G1
Time Value of Money Math
Practice #3
What will Nicole’s investment be worth at the
end of five years?
$10,408.08
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 26
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #4
Robert opens an account at a local bank. The
account pays 2.4% interest compounded
monthly. He deposits $100 every month for
three years. How much is in the account
after three years?
What is the equation?
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 27
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Time Value of Money Math
Practice #4
Step One: Divide nr
.024
12
Step Two: Add 1
1
.002
100
1
1.075
1.075
Step Five: Multiply by principal
.075
1.002
Step Four: Subtract 1
Step Three: Multiply
by exponent
(12x3)
1.002
.002
7.5
.075
Step Six: Divide by rn
7.5
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 28
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
.002
2.4.2.G1
2.4.2.G1
Time Value of Money Math
Practice #4
What will Robert’s investment be worth at the
end of three years?
$3,750.00
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 29
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #5
When Daisy turned 15, her grandparents put
$10,000 into an account that yielded 4% interest,
compounded quarterly. When Daisy turns 18, her
grandparents will give her the money to use
toward her college education. How much will
Daisy receive on her 18th birthday?
What is the equation?
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 30
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #5
Step One: Divide nr
.04
4
.01
Step Three: Multiply
by exponent
(4x3)
1.01
1.127
Step Two: Add 1
1
.01
1.01
Step Four: Multiply by
principal
1.127
10,000
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 31
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
11,270
2.4.2.G1
Time Value of Money Math
Practice #5
How much will Daisy receive on her
18th birthday?
$11,270
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 32
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Practice calculating by
entering all variables into
the formula (advanced
calculator)
Use with Time Value of Money
Math Practice – Advanced
Calculator Worksheet
Remember PEMDAS? When entering
formulas into an advanced calculator,
the order of operations matters. Use
parenthesis to group your variables.
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 33
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #1
Camila deposited $600.00 into a savings account one
year ago. She has been earning 1.2% in annual simple
interest. Complete the following calculations to
determine how much Camila’s money is now worth.
Identify the variables
P = 600
r = 1.2% =.012
t=1
On the calculator, you can save
a step. By modifying the
formula slightly, you can add
the principal while making the
interest calculation.
FV = P(1+r)t
Enter the whole formula at once:
600(1+.012)(1)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 34
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #1
How much is Camila’s investment
worth after one year?
$607.20
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 35
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #2
Felipe’s grandparents have given him $1500.00 to
invest while he is in college to begin his retirement
fund. He will earn 2.3% interest, compounded
annually. What will his investment be worth at the
end of four years?
Identify the variables:
What is the equation?
P = 1500
r = 2.3% =.023
n=1
t=4
Enter the whole formula at once:
1500(1+.023/1)^(1x4)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 36
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #2
What will Felipe’s investment be worth at the end
of four years?
$1642.83
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 37
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #3
Nicole put $2000.00 into an account that pays 2%
interest and compounds annually. She invests
$2000.00 every year for five years. What will her
investment be worth after five years?
Identify the variables:
What is the equation?
P = 2000
r = 2% =.02
n=1
t=5
Enter the whole formula at once:
2000((1+.02/1)^(1x5)-1)/(.02/1)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 38
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #3
What will Nicole’s investment be worth at the
end of five years?
$10,408.08
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 39
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Time Value of Money Math
Practice #4
2.4.2.G1
Robert opens an account at a local bank. The
account pays 2.4% interest compounded
monthly. He deposits $100 every month for three
years. How much is in the account after three
years?
Identify the variables:
What is the equation?
P = 100
r = 2.4% =.024
n = 12
t=3
Enter the whole formula at once:
100((1+.024/12)^(12x3)-1)/(.024/12)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 40
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #4
What will Robert’s investment be worth at the
end of three years?
$3,728.90
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 41
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
Time Value of Money Math
Practice #5
2.4.2.G1
When Daisy turned 15, her grandparents put
$10,000 into an account that yielded 4% interest,
compounded quarterly. When Daisy turns 18, her
grandparents will give her the money to use
toward her college education. How much will
Daisy receive on her 18th birthday?
Identify the variables: What is the equation?
P = 10,000
r = 4% =.04
n=4
t=3
Enter the whole formula at once:
10000(1+.04/4)^(4x3)
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 42
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona
2.4.2.G1
Time Value of Money Math
Practice #5
How much will Daisy receive on her
18th birthday?
$11,268.25
© Take Charge Today – June 2016 – Time Value of Money Math – Slide 43
Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona