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 Engineering Economy

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PostSubject: Engineering Economy   Sat Jan 02, 2010 2:05 am

Engineering Economy
The following variables will be used throughout the presentation


P = Principal (Present Sum)

S = Future Sum

N = Number of Payments

I = Interest Rate


Simple Interest


Equation: S = P + N I P = P (1 + N I)
Example: If $100.00 was deposited at 6% yearly interest, your account would have these balances after each year.


Year Balance
0 100.00
1 106.00
2 112.00
3 118.00
4 124.00


Compound Interest
"Interest on the Accrued Interest"
Equation: S = P (1 + I)^N

Example: If $100.00 was deposited at 6% interest and compounded annually, your account would have these balances after each year:

Year Balance Equation

0 100.00 P
1 106.00 P(1+I)^1
2 112.36 P(1+I)^2
3 119.10 P(1+I)^3
4 126.25 P(1+I)^4


Example: If you deposit $2000.00 today at 7% interest compounded annually, what will be the balance in 3 years?





Compound Interest Time Line


"Backward Time"
Example:If $4000.00 is needed in 3 years, how much money should be deposited today, assuming 7% interest compounded yearly?




Solution: P = Present Value = S (1 + I)^-N
= $4000.00 (1 + 0.07)^-3
= $3265.19



References:

Lecture written by: Dr. Larry Genalo

Authored for presentation by: David Kilzer

Revised by Mark Sobek and Lex Jacobson

HTML documentation by: Larry Genalo Jr.

Date last updated: 8/1/95
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Join date : 2009-10-27
Location : UNITED STATE OF AMERICA, STATE COLLEGE,PA

PostSubject: Re: Engineering Economy   Sat Jan 02, 2010 10:38 pm

[size=12][font=Times New Roman]Tips for Doing Problems


When doing engineering economy problems, make sure:

"TIME FRAMES" MATCH:
If one period equals one quarter, then the interest rate should be quarterly and compounded quarterly. For example, if a yearly interest rate is given but interest is compounded monthly, divide the interest rate by 12.

ANSWER IS REASONABLE

ANSWER IS ROUNDED TO THE NEAREST PENNY


Sinking Fund




Definition: A sinking fund differs from compound interest in that we now have uniform payments over time in addition to the compound interest.




Sinking Fund Time Line


Example #1
Example: If you deposit $50 per month into an account that pays 6% interest, compounded monthly, for 2 years, how much is in the account immediately after the last deposit?



Please Note: Yearly interest in the equation is divided by 12 since payments are on a per-month basis.
Also Note: There are 24 payments, not 23 months.



Sinking Fund Time Line


Example #2

Example: Which is of more value to receive:
(a) $8000 today or
(b) 5 annual payments of $2000, beginning in 1 year?
(Assume 8% interest compounded annually.)



Sinking Fund Time Line
Example #3
Example: Which is of more value to receive:
(a) $8000 today or
(b) 5 annual payments of $2000, beginning in 1 year?
(c) 5 annual payments of $2000, beginning today?
(Assume 8% interest compounded annually.)



Annuity
NOTE: Follow the algebraic steps used to find the present value of a sinking fund. This is the formula for an annuity.

http://www.eng.iastate.edu/efmd/Captures/annline1.gif


APPLICATION: The first application of the annuity formula is to find the present value of a sinking fund. The second is using the formula in situations like the following example.

EXAMPLE: You borrow $5000 to buy a car. If you repay the loan with 36 monthly installments at 18% interest, what is the amount of each payment?




Summary

Compound Interest


Equation: S = P (1 + I)^N



Sinking Fund
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