Transcript Review - College of Engineering | SIU

Our First Magic Number
• F/P i,n
• Formula is (1 + i)n
• The effect of F/P is to take a present number
of dollars and move them n compounding
periods into the future at a rate of return (or
interest rate) of i
• F/P * Present Value = Future Value
Example of Use
• Lanna Loaner is using student loans to
finance the cost of her college education.
Lanna figures she will take 5 years to
graduate. She figures that she will take 12
hours each semester (except summer).
– Lanna figures each semester will cost $1,820 in
tuition and fees
– Lanna expect to spend $500/semester in books
and supplies
Lanna’s Learning Legend
• Lanna figures she will spend $475/month
on university housing (for 9 months of the
year - she’ll live at home and work during
the summers).
• Lanna figures she will need $400/month for
food and clothing
• Lanna figures she can save $5,000 each
summer from working.
Lanna Loves Learning
• Lanna arranges to get student loans
sponsored by the government Future
Income Tax Enhancement Agency. The
loans will be made yearly with interest a 6%
compounded annually.
• How much debt will Lanna accumulate by
the time she graduates?
Step #1
• Turn the story problem into a cash flow.
• Figure out what Lanna needs in loans every
year
– 2 semesters tuition and fees
• $1820 * 2 = $3640
– 2 semesters books and supplies
• $500 * 2 = $1000
– 9 months housing
• $475 * 9 = $4275
– 9 months food and clothing
• $400 * 9 = $3600
Continuing Step #1
• Total up Lanna’s expenses
– $3640 + $1000 + $4275 + $3600 = $12,515
• When Lanna starts college she probably
won’t already have a pile of money saved,
so she will have to take the full loan the first
year - thereafter
• Credit Lanna’s earnings in the summer
– $12,515 - $5000 = $7,515
Making my Cash Flow
• First decision - Who’s perspective will I
take (I have Lanna taking the loan and the
bank giving it out).
• I’m going to take Lanna’s
• At the beginning of each school year Lanna
sees money moving into her pocket
– We use the convention that money moving in
our pocket is positive - money moving out is
negative.
Drawing a Pretty Picture
$12,515
$7,515
$7,515
$7,515
$7,515
5 - Lanna Gets Her Diploma
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How Big a Hole will
Lanna be in?
Going to the Next Step
• Using magic numbers to “sweep up” all the
money into one pile
• I’m will use F/P magic number because I
want to sweep dollars from the present into
one pile in the future
Apply F/P Magic Numbers
We need to sweep this number ahead 5 interest
periods into the pot of money Lanna will owe
$12,515
5 - Lanna Gets Her Diploma
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Pick Out the Number to Use
• I need an F/P magic number because I have
a present dollar amount I want to sweep into
the future pot.
• I need it to be an F/P i, 5 because I want to
sweep 5 compounding periods into the
future
• I need it to be an F/P 6, 5 because my interest
rate each year is 6%
Apply the formula to get my
Magic Number
• (1 + 0.06) 5 = 1.33823
• The formula I used is (1 + i ) n
Moving Along to My Next
Number
$12,515 * 1.33823
I now want to sweep this money into the future
pot.
$7,515
5 - Lanna Gets Her Diploma
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F/P Magic number needed
I need to move 4 compounding periods
I need 6 % interest
Calculate My Magic Number
• (1 + 0.06 ) 4 = 1.26248
• Note that this number is smaller than
1.33823
• Reality Check - Does it make sense that if
money doesn’t have as long to earn interest
that it will earn less interest?
– Yes so we’re probably still on the right track
Next Number
How many periods do I need
to sweep this one and this one
$12,515 * 1.33823
$7,515 * 1.26248
5 - Lanna Gets Her Diploma
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I need to sweep this number 3 compounding
periods into the future.
Now for the Last Step
$12,515 * 1.33823
$7,515 * 1.26248
$7,515 * 1.19102
$7,515 * 1.1236
$7,515 * 1.06
5 - Lanna Gets Her Diploma
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Now we will add up all the numbers
to sweep them into the pot.
Adding Up the Numbers
• $12,515 * 1.33823 = $16,748
–
–
–
–
$7,515 * 1.26248 = $9,488
$7,515 * 1.19102 = $8,950
$7,515 * 1.1236 = $8,444
$7,515 * 1.06 = $7,966
• Total swept into the future debt pot is
– $51,596