Engineering is $$$

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## Engineering is $$$

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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**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**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?**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?**Compound interest—different forms**Interest compounded once per year Interest compounded q times per year Interest compounded continuously**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**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**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?**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,**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**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.