Business Math

For Problems 1-5, assume you deposit $1,500 today in a savings account. You earn 7.5%, compounded semi-annually. You deposit an additional $250 at the end of each 6 months. At the end of 5 years, you withdraw the balance of $5,134.53. Identify each value.

1) n?

A 5 B 10 C 2.5 D 60

2) i?

A 7.5% B 15% C 3.75% D 0.625%

3) PV?

A $1,500 B $250 C $2,500 D $5,134.53

4) PMT?

A $1,500 B $250 C $2,500 D $5,134.53

5) FV?

A $1,500 B $250 C $2,500 D $5,134.53

For Problems 6-8, assume you purchased some corporate stock 4 years ago for $7,500. You received quarterly dividends of $75; your dividends total $1,200 (16 dividend checks ? $75 = $1,200). You sold the stock today for $8,050.

6) The PV is $8,050 because that is the amount you received today (in the present). (T or F)

A True B False

7) $1,200 represents which variable?

A PV B PMT C FV D None of the variables

8) What is the FV amount?

A $7,500 B $1,200 C $550 D $8,050

Unit 12.2 Financial calculators

9) If the upcoming problem is merely a variation of the previous problem, it is easier to change the values that are different, rather than clearing all registers and re-entering all values. (T or F)

A True B False

10) By setting our ?periods per year? register at 1 we must enter the periodic rate in the i-register. (T or F)

A True B False

11) We can review the values in the TVM registers by simply pressing the key of the value we want to review. (T or F)

A True B False

12) Values can be entered in the TVM registers in any order. (T or F)

A True B False

13) When entering dollar amounts in the PV, PMT, and FV registers, we should enter amounts paid as positive numbers, and amounts received as negative numbers. (T or F)

A True B False

14) Suppose you are entering a negative $300 in the PMT register. Keystrokes are:[ – ] 300 [PMT]. (T or F)

A True B False

15) If you make a total of ten $50 payments, you should enter $500 in the PMT register. (T or F)

A True B False

Unit 12.3 Future value

16) 150 years ago, your great-great-great-grandmother stuffed $55 under her mattress . If she had instead invested the money earning 3% compounded quarterly, how much money would she have today?

A $641,800.60 B $302.50 C $4,868.50 D $4,633.90

17) Gregg Levan is 45 years old and deposits $1,000 at the end of every 6 months into an individual retirement account (IRA). If the account earns 6.45% compounded semi-annually, how much will Gregg have when he retires 22 years later?

A $45,822.17 B $94,307.96 C $227,073.10 D $508,640.18

18) Annie O?Malley just turned 19. She decides to save $1 a day and set it aside in a money pouch in her closet. Then, at the end of each year, Annie will deposit the $365 in a savings plan that earns 4.77% compounded annually. How much will Annie have when she turns 50, after her final deposit?

A $24,790.91 B $3,750.94 C $10,895.13 D $70,984.06

19) Morgan spends $185 a month on sodas and is considering the advantages of drinking water instead. If Morgan just turned 24 and deposits the $185 at the beginning of each month into a savings plan earning 3.5% compounded monthly, how much will she have in her savings plan at age 60?

A $159,086.57 B $159,547.92 C $159,774.16 D $160,240.17

20) Refer to Problem 19. How much will Morgan have if the deposits are made at the end of each month?

A $159,086.57 B $159,547.92 C $159,774.16 D $160,240.17

21) Refer to problem 20. How much interest will Morgan?s savings plan earn?

A $159,774.16 B $79,854.16 C $160,240.17 D $80,320.17

22) If you deposit $100 at the end of each month earning 5.75% compounded monthly, what will your balance be in 40 years?

A $187,039.00 B $186,147.04 C $14,536.85 D $48,000

23) The average growth rate for a certain blue chip stock over the last 100 years is 10.5%. If your great-great-grandfather had invested $90 in the stock 100 years ago and received the 10.5% return, what would his investment be worth today?

A $90.95 B $184.50 C $1,951,957.29 D $18,589,212.32

24) Tuition at a local college is currently $3,220 per year. You want your newborn son to attend when he turns 18. If tuition rates are expected to increase at an annual rate of 6%, what will the annual tuition be at the college 18 years from now?

A $9,190.97 B $3,477.60 C $6,697.60 D $99,516.20

25) Suppose there are an estimated 3,700 gorillas in a certain region. If the gorilla population is decreasing 4% per year, what will the gorilla population be 25 years from now?

A 0 B 9,863 C 1,333 D 1,281

Unit 12.4 Present value

26) Brian?s uncle gives all of his nieces and nephews $4,000 on their 30th birthdays. Brian just turned 21. What is the value of the $4,000 gift, in today?s dollars, assuming that Brian can earn 8.3% compounded annually?

A $1,951.66 B $8,198.15 C $365.77 D $749.66

27) Neal Surami, an author from Japan, sells the movie rights to his book and will receive 6,000,000 yen at the end of each 6-month period for the next 6 years. Assuming that money is worth 4.35% compounded semiannually, what is the present value of the movie rights?

A 81,269,092.09 yen B 62,775,423.52 yen
C 31,097,579.66 yen D 148,721,333.52 yen

For Problems 28-31, assume you own a manufacturing business and are thinking about purchasing a labor-saving device at a cost of $267,000. The device will last 12 years and save you $2,110 per month in labor costs (assume that the savings are realized at the end of the month).

28) If you buy the device, what is the total amount of labor costs you will save?

A $25,320 B $303,840 C $36,840 D $570,840

29) Having the answer to Problem 28 is all that you need to decide if you should buy the device? (T or F)

A True B False

30) Assuming that you need to earn 7.8% compounded monthly on your money, what is value of the device?

A $70,082.85 B $267,000 C $196,917.15 D $463,917.15

31) Should you buy the device?

A Yes, because the value of the device is greater than its cost.
B Yes, because the total amount of money you will receive is greater than its cost.
C No, because the value of the device is greater than its cost.
D No, because the value of the device is less than its cost.

32) You have the chance to buy a promissory note in which you will receive 85 monthly payments of $880, starting a month from now. If you buy the note, what is the total amount you will receive?

A $74,800 B $748,000 C $7,480 D $7,480,000

33) Refer to Problem 32. If you want to earn 8% compounded monthly, what price should you pay for the note?

A $5,984 B $10,984.14 C $56,960.41 D $57,340.15

34) Four years ago you bought a 25-year 8.5% $1,000 bond. The bond pays interest each 6 months. You want to sell the bond. You just received the 8th semiannual interest payment of $42.50 ($1,000 x 4.25% periodic rate = $42.50). Similar bonds are being issued that pay 6% semiannually. What is your bond worth today?

A $1,296.27 B $1,000 C $1,321.62 D $902.44

35) Refer to Problem 34. Which statement is true?

A Your bond is worth less than $1,000 because the coupon rate is less than the 6% prevailing rate.
B Your bond is worth more than $1,000 because the coupon rate is less than the 6% prevailing rate.
C Your bond is worth less than $1,000 because the 6% prevailing rate is less than the coupon rate.
D Your bond is worth more than $1,000 because the coupon rate is greater than the 6% prevailing rate.

36) Some bonds, referred to as zero-coupon bonds, pay no periodic interest; instead the bondholder buys the bond at a discount and receives the maturity value on the maturity date. In effect, interest is received in one lump-sum when the bond matures. Suppose a corporation issues 25-year $1,000 zero coupon bonds. Calculate the price you must pay for one of these bonds based on a prevailing 7% annual rate.

A $70 B $930 C $112.93 D $184.25

37) You rent an apartment for $850 a month and offer to prepay 12 months? rent. If the landlord can earn 8.4% compounded monthly, what amount should the landlord accept? (Remember, rent is always paid in advance, at the beginning of each month.)

A $9,750.67 B $9,818.93 C $10,676.22 D $10,602.01

Challenge problems

38) You invest $1,400 today in a savings plan earning 5.5% compounded quarterly. You then invest $100 each quarter (starting in 3 months). What will your balance be at the end of 7 years?

A $5,439.45 B $2,863.24 C $12,592.33 D $$6,928.44

For Problems 39-42, consider Social Security and Medicare payroll deductions. As of December, 2015, the federal government requires employees to pay tax of 7.65% on the first $118,500 earned each year plus 1.45% of the remainder. Employers must contribute a matching amount. Assume that an employee earns $55,000 each year during a 40-year working career.

39) Based on these rates, what is the amount withheld from the employee?s pay each year?

A $7,803 B $1,479 C $797.50 D $4,207.50

40) What is the total amount contributed by the employee and employer each year?

A $15,606 B $2,958 C $1,595 D $8,415

41) The money is remitted to the government quarterly. What is the quarterly deposit?

A $3,901.50 B $739.50 C $398.75 D $2,103.75

42) Assuming that the deposits were made to a savings plan at the end of each quarter (instead of with the IRS), earning 7.5% compounded quarterly, how much would the employee have in the savings plan at the end of a 40-year working career?

A $2,079,657.61 B $478,090.90 C $2,091,360.11 D $2,068,027.20

43) An accomplished violinist lost her right hand in an accident. She successfully sued the party responsible. You, as a member of the jury, are trying to decide what amount the violinist should receive as a settlement. You have determined that the violinist was able to earn $40,000 net income from concerts each month and would have been able to continue earning that amount for another 18 years. Assuming that money is worth 6.5% compounded monthly and that the $40,000 was received at the end of each month, what is a fair settlement?

A $5,085,426.99 B $16,333,556.02 C $16,422,029.45 D $5,112,973.06

44) You leased retail space 7 years ago for $17,500 per month, payable at the beginning of each month. Your lease is for 20 years and allows you to sublease the space. You have outgrown the space and sublease to Rest Easy Mattress for the remaining 13 years. Rest Easy will pay you $23,500 per month. What is the value of your position in the lease (referred to as a leasehold interest), assuming that money is worth 8.25% compounded monthly?

A $573,023.96 B $2,244,343.86 C $2,259,773.73 D $576,963.50

45) You win a $20 million lottery. When you go to collect your money, you find out the $20 million will be paid with 10 annual payments of $2 million, starting today. What is the real value of your prize, in today?s dollars, assuming that you can earn 9% compounded annually?

A $13,990,493.79 B $12,835,315.40 C $8,448,216.14 D $8,198,874.59

46) Refer to Problem 45. If you invest the lottery payments in a savings plan, earning 9% compounded annually, how much will you end up with at the end of year 10?

A $47,347,273.49 B $30,385,859.44 C $33,120,586.78 D $80,467,860.28

47) Sofie Strauss, a 34-year-old nurse, decides to start a retirement plan. She figures that her income for the next 20 years will be sufficient to deposit $1,200 at the end of each quarter into her retirement plan earning 6.35% compounded quarterly. After 20 years she will let the money sit for another 12 years, without making additional deposits, until she is 66 years old. What amount will Sofie have when she turns 66?

A $190,904.61 B $193,935.22 C $413,037.79 D $406,583.27