# Lesson 5.4 PRT Formula

```Problem of the day….
• You have to pay the first
\$500 of car repairs following
an accident. The money
you pay is called your:
Saving money is an important
part of financial freedom and
responsibility.
having a savings account?
Brainstorm Ideas!
Anticipation- where does all that
money come from???
• Simple ways to save money
• Using your smart phone to save money– justify that expensive
phone
• Can you come up with more?
WHY SAVE MONEY?
A little goes a long way…
• Person 1 (age 18) puts
away \$3,000 per year in
her Individual Retirement
Account (IRA) earning
10% - she does this for
10 years then stops.
• She accumulates
\$1,239,564 by the age of
65.
• 3000 x .10 x 10 years
• Money continues to grow
47 years



Person 2 waits until
he is 28. He
contributes \$3,000 to
his IRA account
earning 10% for 37
years.
He accumulates
\$1,102,331 by the
age of 65.
3000 x .10 x 37
years
Time Value of Money
• Time value of money -- Money to be paid out or
received in the future is not equivalent to money
Rule of 72
8% x no. of years = 72
TIME NEEDED FOR MONEY TO
DOUBLE
OR 72 DIVIDED BY THE RATE
\$1,000 AT 8% WILL DOUBLE
IN APPROXIMATELY 9 YEARS
Examples: @ 2% years to double =
Example: @ 4% years to double =
36 years, 18 years
Which would you rather have? Million dollars
or a penny that doubled it’s value everyday?
A few years back I was having a conversation with some people on
how whenever you decide to invest in something for the long term,
you should always think ahead on what would be the best choice in
the long run while having persistence to follow through with it. The
scenario was that if you were given a choice to receive one million
dollars in one month or a penny doubled every day for 30 days,
which one would you choose? When I first heard this, I knew that
the penny doubled everyday must have been the better choice to
go with as it was a little obvious to me that it had to be a trick
question of some sort. But how much better would it be was not
something that I knew immediately. So to demonstrate this, it was
actually written out with all the calculations and it turned out to
something like this:
•
•
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•
•
•
•
•
•
•
•
•
•
•
Day 1: \$.01
Day 2: \$.02
Day 3: \$.04
Day 4: \$.08
Day 5: \$.16
Day 6: \$.32
Day 7: \$.64
Day 8: \$1.28
Day 9: \$2.56
Day 10: \$5.12
Day 11: \$10.24
Day 12: \$20.48
Day 13: \$40.96
Day 14: \$81.92
•
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•
•
•
•
•
•
•
•
•
•
•
•
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Day 15: \$163.84
Day 16: \$327.68
Day 17: \$655.36
Day 18: \$1,310.72
Day 19: \$2,621.44
Day 20: \$5,242.88
Day 21: \$10,485.76
Day 22: \$20,971.52
Day 23: \$41,943.04
Day 24: \$83,886.08
Day 25: \$167,772.16
Day 26: \$335,544.32
Day 27: \$671,088.64
Day 28: \$1,342,177.28
Day 29: \$2,684,354.56
Day 30: \$5,368,709.12
Time Value of Money: Money is worth more in the future, than what it is
worth today.
This all boils down to one concept:
Patience
Lesson Objective
Calculate simple interest and the amount.
Content Vocabulary
Interest ( I )
interestinterest rate
simple
principal
annual
simple interest
Interest
The
amount
percent
paid of
only
money
theon
principal
the
paid
for the use
original
earning
earned
as
principal.
interest.
interest
of a lender’s
in one
money.
year.
Principal (P)
annual interest rate (R)
Time (T)
The amount of time for which the principal is
borrowed or invested. (How long was the money
in the bank?)
When you calculate time in an equation, it must be written as “part
of a year” if it is less than a year.
Examples:
3 months 3/12______
7 months __7/12____
15 days _15/365_____
26 days __26/365____
\$1,000 Invested at 10%
Simple Interest Rate
1 Year
2 Years
\$1,100.00
\$1,200.00
AMOUNT
• If the interest is computed and deposited into the
account, the new quantity is called the amount.
Amount = Principal + Interest (A = P + I)
Interest = Principal x Rate x Time (I = PRT)
Example:
• You open a savings account and deposit \$9,000. Your bank
advertises a 5.5% annual interest rate. If you don’t make any
deposits or withdrawals, how much interest will you make in 3
years?
Principal (\$_9000__) x Rate (__5.5_%) x Time (_3 years)
1. Convert the rate to a decimal: _______% = _.055_____
2. If the “Time” is less than a year, write it as part of a year
(this example is not)
3. Multiply the Principal x Rate x Time:
\$__9000___ x __.055__ x 1____ = \$___495____
• You will make \$__495___ interest in 1 year.
4. Find the “Amount” = P + I
Principal (\$__9000) + Interest (\$_495_) = \$_9495_
Using the same example, how much interest
will you earn at the end of 3 months?
Interest = P (\$_9000__) x R (.055) x T (__3/12___)
remember it is part of a year
\$_9000 x .055 x 3_&divide; 12_= \$_123.75_ (interest for 3 months)
• Amount = \$_9000___ + \$123.75_ = \$__9123.75
Using the same example, calculate the interest
earned for 3 days.
Interest = P (\$_9000_) x R (_5.5%) x T (3/365)
\$__9000 x _.055 x _3_ &divide; _365_ = \$_4.07_
Interest = \$__4.07___(round final answer to a dollar amount)
Amount: \$_9000 + \$_4.07___= \$_9004.07_
Closure:
WHAT GIVES YOU THE BEST
RETURN ON INVESTMENT?
MONTHLY OR DAILY
COMPOUNDING
Assignment:
• p. 224 (5-14)
**for #8 use 15
12
5a. \$216 b. \$936
6a. \$18 b. \$738
7a. .59
b. \$720.59
8a. \$506.36 b. \$6,398.51
9a. \$232.57 b. \$27,201.01
10. \$760 x .05 x 3/12 = \$9.50
11. \$2,430 x .0675 x 65/365 = \$769.50
12. 618.75 = 15,000 x .055 x T/12
618.75 = 825T
12
Multiply both sides by 12: 7425 = 825T
Divide each side by 825: 9 = T (9 months)
13. 10,000 = P x .0475 x 90
365
10,000 = .0117123288 P
P = \$853,801.1672 = \$853,801.17
14. \$75,760 – 73,000 = \$2760 (this is the interest)
\$2,760 = \$73,000 x .075 x T
12
\$2,760 = 456.25 T
6.049314068 (6 months)
March 1 plus 6 months = September 1
#15 Warm-up
9,364.85 x .04 x 5/ 365 = 5.13
8,364.85 x .04 x 12/365 = 11.00
6364.85
x .04 x 10/365 = 6.98
4364.85 x .04 x 3/365 = 1.44
Total 24.55
30 days of activity
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