Inflation / Deflation. Inflation is an increase over time in the price of a good or service with a constant value A gallon of 87 octane gasoline increases in price (but still only gets Dr. J. 32 miles down the road)
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Inflation / Deflation
Other Examples:
Average Inflation Rate (f)
Deriving Equation for Inflation
P = 50,000
f = 10% increase annually
F1 = 50,000 + 50,000 (.10) = 50,000 (1 + .10) = 55,000
F2 = 55,000 + 55,000 (.10) = 55,000 (1 + .10)
= 50,000 (1 + .10)(1 + .10)
= 50,000 (1 + .10)2 = 60,500
F3 = 60,500 + 60,500 (.10) = 50,000 (1 + .10)2(1 + .10)
= 50,000 (1 + .10)3 = 66,550
Generally:Fn = P (1 + f )n
Constant Dollars vs. Actual Dollars
$A = $C (1+ f )n
$C = $A (1+ f )– n
1980
2012
ACTUAL
$
$785 / QTR Tuition & Fees
$785 (1+ f )32 / QTR Tuition & Fees
Constant Dollars vs. Actual Dollars
1980
2012
CONSTANT
$
$785 / QTR Tuition & Fees
$785 / QTR Tuition & Fees
f = Average Inflation Rate
Incorporating Inflation
Real Life Examples
OSU research proposal budgets were supposed to contain a 4% cost increase factor for each successive year.
e.g. If I have a grad student helping with my research, for each year I employ her, I will need to figure a 4% increase in her stipend, her tuition waiver, her insurance contribution, …
What happens if we use a 4% average inflation rate for some common student-oriented prices?
1979
2012
$0.799 / gal
$0.799 (1+ 0.04 )33 = $2.92 / gal
F33 = $0.799 (F/P, 4%, 30) (F/P, 4%, 3)
= $0.799 (3.2434) (1.1249)
= $2.92 / gal
Example 1
Dr. J. used a motorcycle to get to college. At the Fall of 1979, the cost of a gallon of gas was 79.9 ¢. What should the cost have been in 2012 at a 4% average annual rate of inflation?
Find:
F33 (19792012)
Given:
P = $0.799 / gal
f = 4%
$3.35 / gal
Hardrockn Depot
(cash price)
July 11, 2012
Actual average inflation rate was 4.4 % / YR
1980
2012
$66.50 / Cr Hr
$66.50 (1+ .04 )32 = $233 / Cr Hr
F32 = $66.50 (F/P, 4%, 30) (F/P, 4%, 2)
= $66.50 (3.2434) (1.0816)
= $233.29 / Cr Hr
Example 2
Dr. J. went to Iowa State University for a B.S. in Computer Engineering. In Fall 1980, his fee card said he had to pay $665 for 15 credit hours of quarterly credit (which converts to $66.50 / sem cr hr). What would that cost be this year at a 4% average annual rate of inflation?
Find:
F32 (1980 2012)
Given:
P = $66.50 / Cr Hr
f = 4%
$114.30 / Cr Hr +$62.40 / Cr Hr (Engineering Fee) = $176.70 / Cr Hr
233.85 / Cr Hr (non-resident) SDSMT Catalog 2011-2012
Actual average inflation rate was 3.2 % / YR at SDSMT, and 5.5 % / YR at ISU
1980
2012
$254.20 (1+ .04 )– 32= $72.46 / QTR
F32 = $254.20 (P/F, 4%, 30) (P/F, 4%, 2)
= $254.20 (.3083) (.9246)
= $72.46 / QTR (2.4% inflation rate)
$254.20 / QTR (381.30 / sem)
SDSMT Fee Descriptions 2011/2012
Example 3
At Iowa State University in Fall 1980, Dr. J’s fee card showed a $120 technology fee. SDSMT’s tablet fee was $381.30 for academic year 2011-2012 (or $254.20 / QTR). What might the SDSMT fee have been back in 1980, using a 4% average annual rate of inflation?
Find:
P(2010 1980)
Given:
F32 = $254.20 / QTR
f = 4%
$120 / QTR paid for programmable TI calculators that were bolted to the tables at ISU…
Looks like 4% inflation rate is roughly right for prices, but maybe pay rates don’t keep up…
$25 000 / YR
1986
2012
$25 000 (1+ 0.04 )26 = $69 312/ YR
F26 = $25 000 (F/P, 4%, 25)(F/P, 4%,1)
= $25 000 (2.6658)(1.0400)
= $69 311/ YR
Example 4
Starting industry salary for Dr. J. as a computer engineer in 1986 was $25 000. Assuming a 4% average annual rate of inflation, what should the starting salary have been at graduation in 2012?
$65 370/ YR BLS low end for SD CpE May 2011
Find:
F26 (19862012)
Given:
P = $25 000 / YR
f = 4%
Computer Engineering salaries increased at a 3.92% inflation rate…
$5.50 / HR
1981
$5.50 (1+ 0.04 )31 = $18.55 / HR
F31 = $5.50 (F/P, 4%, 30)(F/P, 4%,1)
= $5.50 (3.2434)(1.0400)
= $18.55 / HR
2012
Example 5
In 1981 Dr. J. worked as a rodman / chainman for a land surveyor. Intern-type pay was $5.50 / HR then. Again, using the 4% average annual rate of inflation, what would the equivalent intern wage have been in the Summer of 2012?
$19.67 / HR average pay for Interns Summer 2011
Find:
F31 (1981 2012)
Given:
P = $5.50 / HR
f = 4%
… and Engineering Intern salaries beat the 4% inflation rate … 4.2% average rate
$3.35 / HR
1981
2012
$3.35 (1+ 0.04 )31 = $11.30 / HR
F31 = $3.35 (F/P, 4%, 30) (F/P, 4%, 1)
= $3.35 (3.2434)(1.0400)
= $11.30 / HR
Example 6
In 1976 Dr. J. got his first job sweeping floors at an aerial photography firm. The National Minimum Wage rose to
$3.35 / HR in 1981, when he quit. Using a 4% average annual rate of inflation, what should the equivalent minimum wage be in the Summer of 2012?
National Min. is $7.25 / HR 01 Jan 2012
$9.04 / HR Washington Min. Wage Law for 2012
(Highest Nationally)
Find:
F31 (1981 2012)
Given:
P = $3.35 / HR
f = 4%
Actual average inflation rate was 2.52% / YR
Concluding Thoughts