The Business of Engineering Making Money is the Bottom Line!

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What are we learning? A large percentage of engineers in the work force today are in management positions. Engineers are able to combine their knowledge of technology with business skills to improve their company by making important and educated business decisions. Plus you make more $$$

Why are we learning it? Your project will not only involve design; it will also involve cost analysis. Everything you learn about Engineering Economics will be used to complete your final project. Your project can be the coolest and most novel idea to hit this planet, but if no one can afford it, it won’t sell.

In the Beginning there was Simple Interest Easiest and oldest form of interest. The amount of interest is easily calculated by multiplying the amount by the interest rate by the number of periods (years or months, usually).

Simple Interest Calculations I = P∙n∙i where... I = accumulated interest P = principal amount (money deposited) n = number of interest periods i = interest rate (as a decimal, not percentage i.e, 0.12 not 12%) per period

Simple Interest Individual Exercise The bank is going to loan you $1000 at 8% interest for 6 years. –What would be the total interest? –How much would you have to repay at the end of the 6 years? (F = final payment or total)

Simple Interest Simplified F = P + I Since I = P∙n∙i → F = P + P∙n∙i → F = P(1 + n∙i)

Compound Interest The Next Level As time moved on, businesses started taking out loans for longer and longer periods of time. Simple interest was applied to the single-interest period, resulting in compound interest.

For the first period, n = 1 and: F 1 = P(1 + i) Compound Interest The First Period

Compound Interest The Second Period The compound interest for the second period is: F 2 = F 1 ∙i = P(1 + i)∙i And the sum at the end of the second period is: F 1+2 = F 1 + F 2 = P(1 + i) + P(1 + i)∙i → F 1+2 = [1 + i]∙P(1 + i) → F 1+2 = P(1 + i) 2

Compound Interest The Third Period The interest for the third period is: F 3 = F 1+2 ∙i = P(1 + i) 2 ∙i And the sum after the third period is: F = F F 3 = P(1 + i) 2 + P(1 + i) 2 ∙i → F = (1 + i)∙P(1 + i) 2 → F = P(1 + i) 3

Compound Interest For n Periods To recap!!! 1 period: F = P(1 + i) 1 2 periods: F = P(1 + i) 2 3 periods: F = P(1 + i) 3 So for n periods: F = P(1 + i) n This is consistent with our previous work.

Same example as before ($1000 at 8% for 6 years), but compounded annually Compound Interest Individual Exercise

Compound Interest Team Exercise What if the same scenario ($1000 at 8% per year for 6 years) was compounded semi-annually instead of just annually? –What are n and i in this example?

Compound Interest: Exercise What’s the Better Deal? Team You have to borrow $6000 from the bank and will pay it back in 5 years. Which is a better deal? –12% compounded monthly? –16% simple interest?

Better Deal 2 $4000 borrowed 3 years 10% interest compounded monthly 12% simple interest 5% interest compounded bimonthly