Download Friday, October 16

Friday, October 13th
Finance
Time is Money
Basic Math Operations First
To remember the conventional order of operations, you can think of
PEMDAS (You might remember this as "Please excuse my dear Aunt Sally.")
• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction
This means that you should do what is possible within parentheses
first, then exponents, then multiplication and division (from left to
right), and then addition and subtraction (from left to right). If
parentheses are enclosed within other parentheses, work from the
inside out.
Here are two examples:
• 3+5x7=?
3 + 5 x 7 = 3 + 35 = 38
•
(1 + 3) x (8 - 4) = ?
(1 + 3) x (8 - 4) = 4 x 4 = 16
Bank Account Math
• Let's go over the math of bank accounts:
Suppose we put $200 in a bank account and
leave it there for a year. The bank account pays
5% interest at the end of each full year. After one
year, after the 5% interest is paid, how much will
be in the account?
• Correct $210.
• That's the $200 we started with, plus 5% of
$200, which is $10
We can formally express it like this:
• At 5% interest, $200 in the bank today will
grow to $210 in one year.
• $200 ×(1.05) = $210
Present Value ×( 1 + Interest Rate )
Future Value
Present Value times (1 + Interest Rate)=
Future Value in One Year
Multiplying $200 by 1.05 is mathematically
equivalent to adding 5% to it.
Let's go to two years. If we leave all
the money in the bank for two
years, how much will we have at
the end?
$220.00 or $220.50
$220.00 is Not correct.
Your original $200 will earn another $10 interest, but
you'll also get interest on the first year's interest.
• Getting interest on interest is called 'compounding.‘
$220.50 is Correct!
After one year you have $210.00.
After the second year, you get 5% of $210,
which is $10.50, in interest.
Your new total is $210 + $10.50 = $220.50.
We can also express it like this:
$200 ×(1.05)² = $220.50 OR
$200 times (1.05 squared)= $220.50
So again..
Present Value times ( 1+Interest Rate ) squared= Future Value
Now, let's do three years. If we leave all the money
in the bank for three years, we have how much?
You tell me?
Here is a hint
To calculate how much we'll have in three years,
we multiply by 1.05 three times, once for the first
year, once for the second year, and once for the
third year. ..
The answer is…
By now, you can probably imagine
the general formula for any
number of years:
• To calculate how much we'll have in a
years, we multiply by 1.05 a times, once
for each year.
Compounding
• If interest is paid and compounded more
frequently than once a year, the formula
gets more complicated, but the basic idea
is the same.
• Our formula, again, is
Future Value = Present Value ×( 1 + Interest Rate )ª,
(1 + Interest Rate ) to the a power
where a is the number of years in the future.
• Using that, we can construct this table, based on a
present value of $200 and an annual interest rate of
5%:
• What would the answer be for year 4, 5 and 6.
Years in the Future (6)
0
1
2
3
200
210
220.50 231.52
4
243.10
5
6
255.26 268.02
How $200 grows at 5% interest per year, compounded annually.
($200×1.05ª) ($200 times 1.05 to the a power)
Now, let's use the same reasoning,
except in reverse, to answer this
question:
How much would you need today
to have $200 in one year? Assume
that your only possible investment
is this 5% bank account.
Which is the correct answer?
$200 or
$200/1.05 = $190.48
0
1
???
$200
2
3
4
5
6
$200 is not correct - You don't need $200 now.You only need the
amount that will grow to $200 if you leave it in the bank and earn
interest for a year.
Correct! You want the amount that will
grow to $200 in one year. You want X such that
X × (1.05) = $200.
Divide both sides of this by 1.05, to get:
X = $200/1.05, which calculates to
X = $190.48.
Let’s take a break
• Then to Present Value and Future Value
• Then Discounted Rates