Engineering Economics 1 year Principal interest earned per period - PowerPoint Presentation

Engineering Economics 1 year Principal interest earned per period end of year value 1 $1,000.00 $100.00 $1,100.002$1,100.00$110.00$1,210.003$1,210.00$121.00$1,331.004$1,331.00$133.10$1,464.105$1,464.10$146.41$1,610.51 P = $1,000.00 n = 5 year i = 10%  

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Engineering Economics 3 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 4 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?   For simple interest, the total value at the end of the term is called the future value F. I = accrued interest P = principal amount (amount of capital)n = number of interest periods (usually months or years)i = interest rate n i  n  Total value after 5 years = $1,000 + $500 = $1,500

Class Problem : 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? 5 Solution: a.   P = Principal Interest n = Number of Interest PeriodsI = Accrued Interesti = Interest rate$3001 Two-Week Period$45?     b.     26 two-week periods in 1 year.   The future value of the loan is $1470, but how much does the loan cost you?   This is an annual simple interest rate of 390%. This rate is not uncommon for quick loan establishments.

Compounding Interest 6 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 2345$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 With simple interest the value was $1,500.When the interest is compounded yearly, the value at the end is $110.51 greater than if simple interest was applied.

Compounding Interest 7 Repeat the problem using Excel and assume monthly compounding.   month principal interest earned per period end of month value 1 $1,000.0023.....60Compare to simple interest and to compounding annually:Simple Interest - $1,500.00Compounded Annually - $1,610.51Compounded Monthly - $1,645.31$1,645.31

Derivation of Future Value for Compounding Interest 8 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 Generalizing for n periods yields . . .   Future worth of initial principal P after n periods with an interest rate of i per period   principal amount interest earned 1 st period interest earned 2 nd period total value after 2 periods       principal amount interest earned 1 st period interest earned 2 nd period interest earned 3rd period total value after 3 periods

Class Problem : 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? 9 Solution:   Comparisons: simple interest F = $1,500.00 interest compounded annually F = $1,610.51 interest compounded monthly F =$1,645.31