Living with the lab Engineering Economics Engineers are often called on to make financial decisions...
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living with the lab Engineering Economics neers are often called on to make financial decisions engineers may serve as managers or even the CEO engineers may review bids from equipment suppliers engineers may need to justify new equipment based on the “rate of engineers make decisions in their own personal lives
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Transcript of Living with the lab Engineering Economics Engineers are often called on to make financial decisions...
living with the lab
Engineering Economics
Engineers are often called on to make financial decisions• engineers may serve as managers or even the CEO• engineers may review bids from equipment suppliers• engineers may need to justify new equipment based on the “rate of return”• engineers make decisions in their own personal lives
Simple Interest
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Simple interest ignores the interest accrued. There is no compounding of interest.
Total value after 5 years = $1,000 + $500 = $1,500
Example: If I loan you $1,000 with an interest rate of 10% per year over a 5 year period, then how much will you owe me after 5 years assuming simple interest?
For simple interest, the total value at the end of the term is called the future value F.
I = accrued interestP = principal amount (amount of capital)n = number of interest periods (usually months or years)i = interest rate
Class Problem – Simple Interest
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You need $300 cash today to pay for some tires for your car, so you visit Fast-Freddie Payday Loans. To get the money, you are required to write a $345 check that Freddie will cash in two weeks.
(a) What is the simple interest rate assuming a loan period of two weeks (n=1)?(b) If you are unable to pay and the interest rate holds for a full year, how much will
the $300 loan cost you?
Solution:
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Compounding Interest
Consider again the problem where I loan you $1,000 with an interest rate of 10% per year over a 5 year period. If the interest is compounded annually, then how much will I owe you after 5 years?
year principal interest earned per period
end of year value
1 $1,000.00
2
3
4
5
$1,100.00
$100.00
$110.00
$1,100.00
$1,210.00
$1,210.00 $121.00 $1,331.00
$1,331.00 $133.10 $1,464.10
$1,464.10 $146.41 $1,610.51
The value at the end is $110.51 greater than if the interest is compounded yearly (see the simple interest problem presented earlier).
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Compounding Interest
Repeat the preceding problem using Excel assuming monthly compounding.
month principal interest earned per period
end of year value
1 $1,000.00
2
3
.
.
.
.
.
60
compare to simple interest and to compounding annually
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Derivation of Future Value for Compounding InterestIt would be a pain to have to manually compute the future value for every problem (as we just did for monthly compounding). We NEED a formula!
interest earned 1st period
interest earned 2nd period+
total value after 2 periods
interest earned 1st period
interest earned 2nd period
interest earned 3rd period+
principal amount
derive F for n=2
principal amount
derive F for n=3
Generalizing for n periods yields . . .
Future worth of initial principal P after n periods with an interest rate of i per period
total value after 3 periods
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Class Problem – Compounding InterestIf I loan you $1,000 with an interest rate of 10% per year compounded monthly over a 5 year period, then how much will you owe me after 5 years?
Comparisons: • simple interest F = $1,500.00• interest compounded annually F = $1,610.51• interest compounded monthly F =$1,645.31
Solution:
