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Engineering is $$$ A dollar today is worth more than a dollar tomorrow: Compound Interest P 0 = principal 0 time units into the future (i.e., today) P n = principal n time units into the future where r is the annual interest rate A Dutchman Peter Inuit bought Manhattan from the

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A dollar today is worth more than a dollar tomorrow:

Compound Interest

P0 = principal 0 time units into the future (i.e., today)

Pn = principal n time units into the future

where r is the annual

interest rate


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A Dutchman Peter Inuit bought Manhattan from the

Canarsie Indians for $23 in 1626. Who got robbed. . .?

Assuming funds were invested at 6% compounded monthly

since 1626. The investment today would be worth

$23*(1+.06/12)(12*(2010-1626)) = $220 *109


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A dollar today is worth more than a dollar tomorrow:

Present Value:

where r is the annual interest rate

US treasury bills sold at “discount”, so that when the bill matures, you receive face value.

If you buy a one-year $10,000 bill with an interest rate of 3%, how much should you expect to pay for it?


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A dollar today is worth more than a dollar tomorrow:

Effective Interest:

Invest $10,000 in company stock. Ten years later, you sell

the stock for $20,000. What was your effective annual rate of

return?


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Compound interest—different forms

Interest compounded

once per year

Interest compounded

q times per year

Interest compounded

continuously



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Lease vs. Buy?

Example: Honda Pilot EX AWD price = $33,595

(Chicago, 2006 figures)

Purchase with 20% down and a 36 month loan @6.75%

down payment = $ 6,719

monthly payment = $ 825

spent after 36 mo = $36,419

residual value = $23,701

total cost = $12,718

Lease for 36 months

down payment = $ 2,000

monthly payment = $ 359

spent after 36 mo = $14,565

residual value = $0

total cost = $14,565


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Annuities: Equal payments paid (or received)

over n time periods

Future value of an annuity:

where Pn = the value of the annuity after n payments of P

Multiply both sides by (1+r) to obtain

Subtract the first equation from the second to obtain


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Annuity example: Each year for 20 years you deposit $1000 into an annuity at an interest rate of 5%. What will be its value in 20 years?


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Annuity example: You win $1M in a lottery which pays you in 20 annual installments of $50K? What’s it worth $$ today, i.e., what is its present value? Assume 5% interest.

but,

So,


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Opportunity Cost

The opportunity cost of a decision is based on what must be given up (the next best alternative) as a result of the decision. Any decision that involves a choice between two or more options has an opportunity cost.

Applications of Opportunity Cost

The concept of opportunity cost has a wide range of applications including:

Consumer choice

Production possibilities

Cost of capital

Time management

Career choice

Analysis of comparative advantage


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Payback Period

The length of time required to recover

the cost of an investment.

Shorter paybacks are better investments.

Problems with this metric:

1. It ignores any benefits that occur after the payback period and, therefore, does not measure profitability.

2. It ignores the time value of money.


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