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Introduction to Business Math
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Introduction to Business Math
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25 Questions

1. What annual percentage rate compounded annually is needed to grow $250000 into $270000 in 6 years?
2. Given five numbers - which of the statements below is always true?
3. Five years from now - a company will have to replace a machine that will cost $2 million. Approximately how much money should the company start putting aside in a bank account at 6% per year to ensure the money for replacement will be available?
4. If a bank charges a discount of 6% for a 6-month loan - what is the equivalent interest rate?
5. A designer signs an agreement to pay a bank $25000 in 5 months. The bank charges a 13% discount rate. Calculate the actual interest rate paid by the designer. Round the final answer to the nearest tenth percent.
6. A real estate agent receives $52000 profit from the sale of some land and invests part at 5% interest and the rest at 4% interest. If the agent earns a total of $2 - 290 interest per year - how much did the agent invest at 4%?
7. A construction company pays its hourly employees $18.50 - $16.50 - $20.50 - $17.50 - and $22.50 per hour. What are the mean and the median hourly rates paid to the employees?
8. A property owner buys a refrigerator for a rental unit for $3 - 500. The book value of the refrigerator is $500 at the end of 5 years. Using the declining-balance method - given that the depreciation rate is twice the rate of the straight-line method - what is the book value at the end of the second year?
9. A worker deposits a promotion bonus of $x in an interest bearing account at rate r1 compounded monthly. Six years later - the rate decreases to r2 - still compounded monthly. Another four years later - the worker consults a financial planner and learns that because of the change to the lower rate the account is now worth only 80% of what it could have been had the higher rate remained in effect for the entire period. What is the incremental difference between rates r1 and r2?
10. Stan bought a 4-year certificate of deposit for $10000 with a rate of 6% compounded semi-annually. How much will he make in interest after 4 years?
11. Kevin is saving for his senior trip. He plans to place $300 in an account every quarter for 2 years with 8% interest compounded quarterly. What will be the final total?
12. A small airline has fixed expenses of $10000 per month and can sell tickets for $250 per seat. The variable costs are $200 per passenger. If the airline starts with 100 tickets sold per month in January and hopes to increase sales by 30 additional tickets each month - what is the first month of the year when it will break even?
13. Minimize z = 3x + 2y - subject to the constraints x + y 100 and 3x + 4y 350 - with x 0 and y 0.
14. After purchasing a wristwatch for $420 on a 15% - 180-day note - a customer pays the note on day 120. How much did the customer save by prepaying the note? Assume a 360-day year and that there are no prepayment penalties.
15. A company designs and sells two types of rings - M and N - and can produce up to 24 rings each day using up to 60 total hours of labor. If it takes 3 hours to make one M ring - versus 2 hours to make one N ring - what is the maximum profit possible - if the profit on a M ring is $30 and on a N ring is $40?
16. Find the effective annual rate corresponding to a nominal annual rate of 12% compounded monthly. Round the final answer to the nearest hundredth percent.
17. An airline charges the following fees based on the weight of a passenger's checked luggage: I. No fee for luggage weighing up to 40 pounds II. Flat fee of $50 for luggage weighing between 40 and 80 pounds III. Additional fee of $1.25 per pound for luggage weighing more than 80 pounds Which of the following graphs represents this situation?
18. A corporation with $250000 annual taxable income has a federal corporate tax rate of 39% and a state corporate tax rate of 4.63%. If state taxes are deductible on the corporation's federal income taxes - then the total annual tax rate for the corporation is
19. Find the effective annual rate corresponding to a nominal annual rate of 8% compounded quarterly.
20. Troglodyte Networks Inc. has 1.5 million shares outstanding and is trading at $20 per share. The P/E ratio is the ratio of the stock price per share to the dividend paid per share and is 10 for Troglodyte. What total amount of earnings is the company expected to pay?
21. The monthly payment on a $61000 loan at 11% annual interest rate is $693.57. How much of the first monthly payment will go toward the principal?
22. Which of the following statements is TRUE for a simple discount note?
23. A company that produces pens sells each for $1.99. Its variable cost per unit is $0.74. What is the contributing margin (CM) and the breakeven point (BE) for the company assuming it has a fixed cost of $75000?
24. Which of these banks should a business use to receive the maximum interest on its deposits?
25. The average weight of a particular mixed fruit bag is 1.81 kg - with a standard deviation of 0.05 kg. If the weights of all the bags are normally distributed - what is the percentage of bags that weigh less than 1.76 kg?