#### Use the rule of 72 to estimate the time it would take for an initial investment of $10,000 to accumulate to $20,000 at a compound rate of 8% per year.

1. A design-build engineering firm completed a pipeline project wherein the company realized a profit of $2.3 million in 1 year. If the amount of money the company had invested was $6 million, what was the rate of return on the investment?

2. A start-up chemical company has established a goal of making at least a 35% per year rate of return on its investment. If the company acquired $50 million in venture capital, how much did it have to earn in the first year?

3. A medium-size consulting engineering firm is trying to decide whether it should replace its office furniture now or wait and do it 1 year from now. If it waits 1 year, the cost is expected to be $16,000. At an interest rate of 10% per year, what would be the equivalent cost now?

4. A company that manufactures regenerative thermal oxidizers made an investment 10 years ago that is now worth $1,300,000. How much was the initial investment at an interest rate of 15% per year (a) simple interest and (b) compound interest?

5. Identify each of the following as either equity or debt financing.

(a) Money from savings

(b) Money from a certificate of deposit

(c) Money from a relative who is a partner in the business

(d) Bank loan

(e) Credit card

6. Use the rule of 72 to estimate the time it would take for an initial investment of $10,000 to accumulate to $20,000 at a compound rate of 8% per year.

7. Pressure Systems, Inc., manufactures high-accuracy liquid-level transducers. It is investigating whether it should update certain equipment now or wait to do it later. If the cost now is $200,000, what will the equivalent amount be 3 years from now at an interest rate of 10% per year?

8. A recent engineering graduate passed the FE exam and was given a raise (beginning in year 1) of $2000. At an interest rate of 8% per year, what is the present value of the $2000 per year over her expected 35-year career?

9. West Coast Marine and RV is considering replacing its wired pendant controllers on its heavy-duty cranes with new portable infrared keypad controllers. The company expects to achieve cost savings of $14,000 the first year and amounts increasing by $1500 each year thereafter for the next 4 years. At an interest rate of 12% per year, what is the equivalent annual worth of the savings?

10. The effort required to maintain a scanning electron microscope is known to increase by a fixed percentage each year. A high-tech equipment maintenance company has offered it services for a fee of $25,000 for the first year (i.e., end of year 1) with increases of 6% per year thereafter. If a biotechnology company wants to pay for a 3-year contract up front to take advantage of a temporary tax loophole, how much should it be willing to pay if it uses an interest rate of 15% per year?

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