living with the lab

1. 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

2. living with the lab Simple Interest I = accrued interest P = principal amount(amount of capital) n = number of interest periods (usually months or years) i = interest rate Simple interest ignores the interest accrued. There is no compounding of interest. 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? Total value after 5 years = $1,000 + $500 = $1,500 For simple interest, the total value at the end of the term is called the future value F.

3. living with the lab • 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. • What is the simple interest rate assuming a loan period of two weeks (n=1)? • If you are unable to pay and the interest rate holds for a full year, how much will the $300 loan cost you? Class Problem – Simple Interest Solution:

4. living with the lab 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? $100.00 $1,100.00 $1,100.00 $110.00 $1,210.00 $121.00 $1,210.00 $1,331.00 $1,464.10 $1,331.00 $133.10 $1,610.51 $1,464.10 $146.41 The value at the end is $110.51 greater than if the interest is compounded yearly (see the simple interest problem presented earlier).

5. living with the lab Compounding Interest Repeat the preceding problem using Excel assuming monthly compounding. compare to simple interest and to compounding annually

6. living with the lab Derivation of Future Value for Compounding Interest It 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! derive F for n=2 derive F for n=3 principal amount principal amount interest earned 1st period interest earned 1st period interest earned 2nd period + interest earned 2nd period + interest earned 3rd period total value after 3 periods total value after 2 periods Generalizing for n periods yields . . . Future worth of initial principal P after n periods with an interest rate of i per period

7. living with the lab Class Problem – Compounding Interest If 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? Solution: • Comparisons: • simple interest F = $1,500.00 • interest compounded annually F = $1,610.51 • interest compounded monthly F =$1,645.31