3. Ashley is planning to attend college when she graduates from high school 7 years from now. She anticipates that she will need $10,000 at the beginning of each college year to pay for tuition and fees, and have some spending money. Ashley has made an arrangement with her father to do the household chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8 percent interest. Will there be enough money in the account for Ashley to pay for her college expenses on the day she starts College? Assume the rate of interest stays at 8 percent during the college years.
No, she needs additional $1,891.46
No, she needs additional $2,043.77
No, she needs additional $4,541.16
No, she needs additional $8,770.19
Yes, she has sufficient funds to cover her expenses.
4. Today is Jan. 1, 2012. Starting today you plan to invest $2000 every year, first deposit today and last deposit on Jan. 1, 2032. After that, you plan to leave the money in the same account until Jan. 1, 2040. However, the interest rate is 6% compounded quarterly until your last deposit and only 9% compounded annually after that. How much money will you have in your account on Jan. 1, 2040?
None of the above
5. You are saving for the college education of your two children. They are three years apart in age; one will begin college in 7 years, and another in 10 years. You estimate your first child’s college expenses to be $30,000 per year, paid at the beginning of each college year (first payment is at year 7 and so on). You estimate your second child’s college expenses to be $50,000 per year, paid at the beginning of each college year (first payment at year 10 and so on). The annual interest rate is 8 percent. How much money must you deposit in an account each year to fund your children’s education? You will begin payments one year from today. You will make your last deposit when your oldest child enters college. Also assume that each child will take 4 years to graduate from college.
None of the above
6. Ken borrows $15,000 from a bank at 10 percent annually compounded interest to be repaid in six equal installments. Calculate the interest paid in the second year.
None of the above
7. Elizabeth has $35,000 in an investment account. Her goal is to have the account grow to $100,000 in 10 years without having to make any additional contributions to the account. What effective annual rate of interest would she need to earn on the account in order to meet her goal?
8. You are currently investing your money in a bank account that has a nominal annual rate of 7 percent, compounded monthly. How many years will it take for you to double your money?
9. Today, Bruce and Brenda each have $150,000 in an investment account. No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $1 million, at which time each will retire. Bruce has his money invested in risk-free securities with an expected annual return of 5 percent. Brenda has her money invested in a stock fund with an expected annual return of 10 percent. How many years after Brenda retires will Bruce retire? Pick the closest answer.
10. Today is your 20th birthday. Your parents just gave you $5,000 that you plan to use to open a stock brokerage account. Your plan is to add $3,000 on your 21st birthday, followed by $4,000 on your 22nd birthday, and $5,000 on your 23rd birthday. How much money do you anticipate that you will have in the account on your 25th birthday, if your account earns 12% interest compounded monthly?
None of the above
11. You have $2,000 invested in a bank account that pays a 4 percent nominal annual interest with daily compounding. How much money will you have in the account at the end of July (in 132 days)? (Assume there are 365 days in each year.)
16. You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?
17. What’s the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?
18. Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?
19. Ms. Day needs $20,000 to buy her dream car. In her search for the best (low cost) loan, she has gathered the following information from three local banks. Which bank would you recommend Ms. Day borrow from?
Bank Annual Payment Term (Years)
A $8,326.40 3
B $6,309.15 4
C $5,411.25 5
Either Bank B and C since their loan rates are the same
Either Bank A and C since their loan rates are the same
20. Your aunt has $500,000 invested at 5.4%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. What is the maximum number of $45,000 withdrawals that she can make and still have at least $50,000 left in the account, right after the last withdrawal? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)
21. A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give the endowment upon her 50th with the first payment on that birthday. She plans to accumulate the endowment by making annual equal deposits into an account from her 40th birthday until her 49th birthday. The rate of interest is expected to be 6 percent in all future periods. How much must the art collector deposit each year to accumulate to the required amount?
22. Otto is planning for his son’s college education to begin ten years from today. He estimates the yearly tuition, books, and living expenses to be $10,000 per year for a four-year degree. How much must Otto deposit today, at an interest rate of 12 percent, for his son to be able to withdraw $10,000 per year for four years of college? Assume first withdrawal on the first day of College (beginning of the year)
23. A ski chalet at Peak n’ Peak now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Chris and Julie retire from successful investment banking careers. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon retirement?
None of the above
24. Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are expected to grow by 5 percent for the next 5 years. How much will Danny have at the end of the fifth year if he invests his Christmas bonuses (including the most recent bonus) in a project paying 8 percent per year?
None of the above.
25. Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?
26. The Bad Guys Company is notoriously known as a slow-payer. It currently needs to borrow $25,000 and only one company will even deal with Bad Guys. The terms of the loan call for daily payments of $30.76. The first payment is due today. The interest rate is 21% compounded daily. What is the time period of this loan?
27. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?
40. Appalachian Airlines began operating in 2006. The company lost money the first year but has been profitable ever since. The company’s taxable income (EBT) for its first five years is listed below. Each year the company’s corporate tax rate has been 40 percent.
Year Taxable Income
2006 -$4 million
2007 1 million
2008 2 million
2009 3 million
2010 5 million
Assume that the company has taken full advantage of the Tax Code’s carry-back, carry-forward provisions and that the current provisions were applicable in 2010. How much did the company pay in taxes in 2009?
41. Scuba, Inc. is concerned about the taxes paid by the company in 2010. In addition to $5 million of taxable income, the firm received $80,000 of interest on state-issued bonds and $500,000 of dividends on common stock it owns in Boating Adventures, Inc. What is Scuba’s tax liability, average tax rate, and marginal tax rate, respectively using the table below?
Taxable Income Tax on Base of Bracket Percentage on Excess above Base
$0-$50,000 $ 0 15%
$50,000-$75,000 7,500 25
$75,000-$100,000 13,750 34
$100,000-$335,000 22,250 39
$335,000-$10,000,000 113,900 34
$10,000,000-$15,000,000 3,400,000 35
$15,000,000-$18,333,333 5,150,000 38
Over $18,333,333 6,416,667 35
(NOT SURE ABOUT THIS)
$1,637,100, 31.788%, 34%
$1,751,000, 34%, 34%
$1,778,200, 34%, 34%
$1,870,000, 34%, 34%
$1,983,900, 36.07%, 34%
42. A 5-year corporate bond yields 9 percent. A 5-year municipal bond of equal risk yields 6.5 percent. Assume that the state tax rate is zero. At what federal tax rate are you indifferent between the two bonds? [Set your calculator to at least four decimal places]
48. Salinger Software was founded in 2009. The company lost money each of its first three years, but was able to turn a profit in 2012. Salinger’s operating income (EBIT) for its first four years of operations is reported below.
2009 -$ 50,000
The company has no debt, so operating income equals earnings before taxes. The corporate tax rate has remained constant at 35%. Assume that the company took full advantage of the carry-back, and carry-forward provisions in the Tax Code, and assume that the current provisions were applicable in 2009. How much tax did the company pay in 2012? Note: Use our criteria for carry back years and forward (what we discussed in our lecture)
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