BA305Midterm Prep4
11) During her four years at college, Hayley received the following amounts of money at the end of each year from her grandmother. She deposited her money in a savings account paying 6 percent rate of interest. How much money will Hayley have on graduation day?
:
12) You have provided your friend with a service worth $8,500. Your friend offers you the following cash flow instead of paying $8,500 today. Should you accept his offer if your opportunity cost is 8 percent?
:
17) 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?
:
32) A lottery administrator has just completed the state's most recent $50 million lottery. Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each year for 10 years. The expenses of running the lottery were $800,000. The state can earn an annual compound rate of 8 percent on any funds invested. (a) Calculate the gross profit to the state from this lottery. (b) Calculate the net profit to the state from this lottery (no taxes).
:
60) To expand its operation, the International Tools Inc. (ITI) has applied for a $3,500,000 loan from the International Bank. According to ITI's financial manager, the company can only afford a maximum yearly loan payment of $1,000,000. The bank has offered ITI, 1) a 3-year loan with a 10 percent interest rate, 2) a 4-year loan with a 11 percent interest rate, or 3) a 5-year loan with a 12 percent interest rate. (a) Compute the loan payment under each option. (b) Which option should the company choose?
: (a) 1) Using financial calculator: PV = 3500000, N = 3, FV = 0, I = 10, CPT PMT = 1,407,402 2) Using financial calculator: PV = 3500000, N = 4, FV = 0, I = 11, CPT PMT = $1,128,304.32 3) Using financial calculator: PV = 3500000, N = 5, FV = 0, I = 12, CPT PMT = $ 970,873.79 (b) The company should choose option #3.
30) A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not be distributed. The grandchild may only receive the interest earned. If the interest rate earned on the trust is expected to be at least 7 percent in all future periods, how much income will the grandchild receive each year?
: $2,000,000 × 0.07 = $140,000
59) Tom is evaluating the growth rate in dividends of a company over the past 6 years. What is the annual compound growth rate if the dividends are as follows:
: ($2.15/$1.38)1/5 - 1 = .0927 = 9.27% Approximately 9 percent.
10) Find the present value of the following stream of a firm's cash flows, assuming that the firm's opportunity cost is 14 percent. A) $131,068 B) $ 19,830 C) $ 14,850 D) $120,820
: A
11) If a United States Savings bond can be purchased for $29.50 and has a maturity value of $100 at the end of 25 years, what is the annual rate of return on the bond? A) 5 percent B) 6 percent C) 7 percent D) 8 percent
: A
11) In comparing an ordinary annuity and an annuity due, which of the following is true? A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity. B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due. C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since one less payment is received with an annuity due. D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due.
: A
11) The rate of interest actually paid or earned, also called the annual percentage rate (APR), is the ________ interest rate. A) effective B) nominal C) discounted D) continuous
: A
14) The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________. A) $253.00 B) $252.00 C) $158.00 D) $134.66
: A
15) The annual rate of return is referred to as the ________. A) discount rate B) marginal rate C) risk-free rate D) marginal cost
: A
15) The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12 percent, is ________. A) $35,098 B) $20,000 C) $39,310 D) $11,300
: A
16) If you expect to retire in 30 years, live on $50,000 per year and expect the inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years? A) $121,363 B) $$95,000 C) $20,599 D) $51,500
: A
19) Assume Julian has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded continuously. Which account provides the highest effective annual return? A) Account A B) Account B C) Both provide the same effective annual return D) We don't have sufficient information to make a choice
: A
23) What is the rate of return on an investment of $124,090 if the company expects to receive $10,000 per year for the next 30 years? A) 7 percent B) 4 percent C) 6 percent D) 5.5 percent
: A
27) A beach house in Southern California now costs $350,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from successful careers in commercial art. 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 beach house upon retirement? A) $11,472 B) $4,323 C) $79,977 D) $17,350
: A
30) Xiao Li wishes to accumulate $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her investments, how much must she deposit at the end of each year? A) $3,975 B) $6,475 C) $5,000 D) $4,513
: A
36) Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is ________. A) $1,155 B) $2,481 C) $ 144 D) $1,327
: A
38) Aunt Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be repaid in 10 equal annual installments. The interest paid in the third year is ________. A) $1,336.00 B) $1,560.14 C) $2,906.11 D) $1,947.10
: A
39) Entertainer's Aid plans five annual colossal concerts, each in a different nation's capital. The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity. The endowment will be given at the end of the fifth year. The rate of interest is expected to be 9 percent in all future periods. How much must Entertainer's Aid deposit each year to accumulate to the required amount? A) $5,569,749 B) $3,333,333 C) $1,830,275 D) $8,568,980
: A
43) How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement? A) 12.2 years B) 15.7 years C) 14.5 years D) 16.5 years
: A
5) The present value of a $25,000 perpetuity at a 14 percent discount rate is ________. A) $178,571 B) $285,000 C) $350,000 D) $219,298
: A
6) An annuity with an infinite life is called a(n) ________. A) perpetuity B) primia C) option D) deep discount
: A
6) The present value of $100 received at the end of year 1, $200 received at the end of year 2, and $300 received at the end of year 3, assuming an opportunity cost of 13 percent, is ________. A) $ 453 B) $ 416 C) $1,181 D) $ 500
: A
8) Find the present value of the following stream of a firm's cash flows, assuming that the firm's opportunity cost is 25 percent. A) $27,168 B) $35,200 C) $34,074 D) $32,281
: A
9) The future value of $100 received today and deposited at 6 percent for four years is ________. A) $126 B) $ 79 C) $124 D) $116
: A
24) Nico is the new assistant branch manager of a larger Florida-based bank and the branch manager has asked him a question to test his knowledge. The question he asked is which rate should the bank advertise on monthly-compounded loans, the nominal annual percentage rate or the effective annual percentage rate? Which rate should the bank advertise on quarterly-compounded savings accounts? Explain. As a consumer, which would you prefer to see and why?
: A bank would rather advertise the annual percentage rate on loans since this rate appears to be lower and the effective annual rate. With respect to savings accounts, the bank would advertise the effective rate since this rate will be higher than the annual percentage rate(APR). As a consumer, the effective rate is the more important rate since it represents the rate actually paid or earned.
56) 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?
: A: Using financial calculator: PV = 20000, PMT = -8326.40, N = 3, FV = 0, CPT I = 12% B: Using financial calculator: PV = 20000, PMT = -6309.15, N = 4, FV = 0, CPT I = 10% C: Using financial calculator: PV = 20000, PMT = -5411.25, N = 5, FV = 0, CPT I = 11% Ms. Day should borrow from Bank B. Bank B has the lowest rate.
23) Assume you have a choice between two deposit accounts. Account X has an annual percentage rate of 12.25 percent but with interest compounded monthly. Account Y has an annual percentage rate of 12.20 percent with interest compounded continuously. Which account provides the highest effective annual return?
: Account X EAR = [1 + - 1 = 12.96% Account Y EAR = - 1 = 12.75% Choose X
38) 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 of the four college years 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? Assume the rate of interest stays at 8 percent during the college years.
: At the beginning of the first year of college: PV = 10,000 + (10,000/0.08) × [1-1/(1.08)3] = 10,000 + 25,770.96 = $35,770.96 PMT = $3,500, r= 8%, n = 7 FVA = 3,500{[(1.08)7-1]/0.08} = 3,500(8.923) = $31,230 Ashley will need $4,541 (= $35,770.96 -$ 31,230) additional money to pay for her college education.
10) The future value of $200 received today and deposited at 8 percent for three years is ________. A) $248 B) $252 C) $158 D) $200
: B
10) The rate of interest agreed upon contractually charged by a lender or promised by a borrower is the ________ interest rate. A) effective B) nominal C) discounted D) continuous
: B
12) The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called ________. A) future value B) present value C) future value of an annuity D) compounded value
: B
12) The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________. A) $28,974 B) $31,291 C) $14,494 D) $13,420
: B
13) Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has priced the cruise at $15,000, and she has 5 years to accumulate this money. How much must Janice deposit annually in an account paying 10 percent interest in order to have enough money to send her parents on the cruise? A) $1,862 B) $2,457 C) $3,000 D) $2,234
: B
13) The future value of $100 received today and deposited in an account for four years paying semiannual interest of 6 percent is ________. A) $450 B) $127 C) $889 D) $134
: B
14) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is ________. A) $11,808. B) $11,464. C) $ 8,530. D) $10,000.
: B
15) The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is ________. A) $17,549 B) $75,401 C) $93,049 D) $11,200
: B
16) Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was ________. A) $24,450 B) $15,000 C) $3,100 D) $20,175
: B
17) If the present value of a perpetual income stream is increasing, the discount rate must be ________. A) increasing B) decreasing C) changing unpredictably D) increasing proportionally
: B
18) Ashley owns stock in a company which has consistently paid a growing dividend over the last five years. The first year Ashley owned the stock, she received $1.71 per share and in the fifth year, she received $2.89 per share. What is the growth rate of the dividends over the last five years? A) 7 percent B) 11 percent C) 12 percent D) 5 percent
: B
19) Julian was given a gold coin originally purchased for $1 by his great-grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to ________. A) 7.5% B) 13% C) 9% D) 18%
: B
20) A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be? A) $ 300,000 B) $3,000,000 C) $ 750,000 D) $1,428,571
: B
21) The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years is approximately ________. A) 5% B) 7% C) 10% D) 12%
: B
22) Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent? A) $120,000 B) $ 67,800 C) $ 38,640 D) $ 72,560
: B
22) What is the rate of return on an investment of $16,278 if the company expects to receive $3,000 per year for the next 10 years? A) 18 percent B) 13 percent C) 8 percent D) 3 percent
: B
25) You have been offered a project paying $300 at the beginning of each year for the next 20 years. What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment? A) $ 2,738 B) $ 2,985 C) $15,347 D) $ 6,000
: B
28) Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment, how much must each deposit be in order to accumulate the $40,000? A) $ 6,132 B) $ 6,684 C) $23,844 D) $ 9,434
: B
3) Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 17 percent on its investments. A) $20,724 B) $20,127 C) $23,550 D) $23,350
: B
32) Detta borrows $20,000 from the bank. For a five-year loan, the bank requires annual end-of-year payments of $4,878.05. The annual interest rate on the loan is ________. A) 6 percent B) 7 percent C) 8 percent D) 9 percent
: B
4) Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 8 percent on its investments. A) $45,000 B) $53,396 C) $47,944 D) $56,690
: C
34) Otto is planning for his son's college education to begin ten years from today. He estimates the end-of-the-year 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? A) $12,880 B) $ 9,780 C) $40,000 D) $18,950
: B
44) What annual rate of return would Jia need to earn if she deposits $20,000 per year into an account beginning one year from today in order to have a total of $1,000,000 in 30 years? A) 2.3% B) 3.3% C) 1.3% D) 4.3%
: B
5) The present value of $1,000 received at the end of year 1, $1,200 received at the end of year 2, and $1,300 received at the end of year 3, assuming an opportunity cost of 7 percent, is ________. A) $2,500 B) $3,044 C) $6,516 D) $2,856
: B
7) The present value of a $20,000 perpetuity at a 7 percent discount rate is ________. A) $186,915 B) $285,714 C) $140,000 D) $325,000
: B
8) ________ is the amount earned on a deposit that has become the part of the principal at the end of a specified time period. A) Discount interest B) Compound interest C) Primary interest D) Future value
: B
22) Jeanne has just graduated from high school and has received an award for $5,000. She would like to deposit the money in an interest earning account until she graduates from college (i.e., four years from now). In her search for the highest interest earning account, she has narrowed the list down to the following two accounts: 1) bank A pays 9 percent interest compounded annually, and 2) bank B pays 8 percent interest compounded semiannually. Which is the better offer, and how much will Jeanne have upon graduation from college?
: Bank A: n = 4, r = 9%, m = 1 FV = 5,000{[(1.09)4 - 1]/.09} = $7,057 Bank B: n = 4, r = 8%, m = 2 FV = 5,000{[1.04)8 - 1]/.04} = $6,842 Jeanne should deposit her money in Bank A and she will have $7,057 upon her graduation from college.
10) Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year? A) $12,290 B) $20,000 C) $31,874 D) $51,880
: C
11) The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is ________. A) $236 B) $699 C) $ 42 D) $ 75
: C
12) If a United States Savings bond can be purchased for $14.60 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond? A) 6 percent B) 7 percent C) 8 percent D) 9 percent
: C
12) The future value of $200 received today and deposited at 8 percent compounded semiannually for three years is ________. A) $380 B) $158 C) $253 D) $252
: C
14) Adam borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is ________. A) $ 942 B) $1,125 C) $1,482 D) $2,641
: C
14) The future value of a dollar ________ as the interest rate increases and ________ the further in the future an initial deposit is to be received. A) decreases; decreases B) decreases; increases C) increases; increases D) increases; decreases
: C
16) A college received a contribution to its endowment fund of $2 million. It can never touch the principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the college earn to help its operations each year? A) $95,000 B) $19,000 C) $190,000 D) $18,000
: C
16) What is the highest effective rate attainable with a 12 percent nominal rate? A) 12.00% B) 12.55% C) 12.75% D) 12.95%
: C
17) Gina has planned to start her college education four years from now. To pay for her college education, she has decided to save $1,000 a quarter for the next four years in a bank account paying 12 percent interest. How much will she have at the end of the fourth year? A) $ 1,574 B) $19,116 C) $20,157 D) $16,000
: C
17) Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was ________. A) $31,000 B) $30,000 C) $25,000 D) $20,000
: C
18) How much would Sophie have in her account at the end of 10 years if she deposit $2,000 into the account today if she earned 8 percent interest and interest is compounded continuously? A) $4,317 B) $4,134 C) $4,451 D) $4,521
: C
21) A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be? A) $2,314,814 B) $2,000,000 C) $3,125,000 D) $3,000,000
: C
24) A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000. At maturity, three years from now, the investor will receive $14,000. What is the rate of return on this investment? A) 14 percent B) 13 percent C) 12 percent D) 11 percent
: C
24) James plans to fund his individual retirement account, beginning today, with 20 annual deposits of $2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be ________. A) $19,636 B) $91,524 C) $98,846 D) $21,207
: C
25) A local bank is offering a zero-coupon certificate of deposit for $25,000. At maturity, three years from now, the investor will receive $32,000. What is the rate of return on this investment? A) 3 percent B) 6 percent C) 9 percent D) 12 percent
: C
31) Dorothy borrows $10,000 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $3,223.73. The annual interest rate on the loan is ________. A) 9 percent B) 10 percent C) 11 percent D) 12 percent
: C
35) Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be repaid in four equal annual installments. The interest paid in the first year is ________. A) $ 152 B) $ 277 C) $ 420 D) $1,152
: C
4) Which of the following is true of annuities? A) An ordinary annuity is an equal payment paid or received at the beginning of each period. B) An annuity due is a payment paid or received at the beginning of each period that increases by an equal amount each period. C) An annuity due is an equal stream of cash flows is paid or received at the beginning of each period. D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period.
: C
40) 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 fiftieth birthday 10 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. 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? A) $1,575,333 B) $ 736,000 C) $1,264,466 D) $ 943,396
: C
42) How many years would it take for Jughead to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement? A) 13 years B) 16 years C) 15 years D) 12 years
: C
45) What annual rate of return would Grandma Zoe need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years? A) 4.55% B) 5.28% C) 5.98% D) 6.23%
: C
5.4 Calculate both the future value and the present value of a mixed stream of cash flows. 1) $100 is received at the beginning of year 1, $200 is received at the beginning of year 2, and $300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________. A) $1,536 B) $ 672 C) $ 727 D) $1,245
: C
8) A(n) ________ is an annuity with an infinite life making continual annual payments. A) amortized loan B) principal C) perpetuity D) APR
: C
10) The time value concept/calculation used in amortizing a loan is ________. A) future value of a dollar B) future value of an annuity C) present value of a dollar D) present value of an annuity
: D
13) The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________. A) $36,050 B) $63,530 C) $40,376 D) $71,152
: D
13) The present value of $200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is ________. A) $ 50 B) $200 C) $518 D) $ 77
: D
15) Jia borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year loan payment is ________. A) $10,774 B) $12,500 C) $14,340 D) $15,773
: D
18) The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________. A) $288 B) $1,896 C) $1,750 D) $1,558
: D
19) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is ________. A) $ 1,020 B) $27,869 C) $18,800 D) $12,093
: D
2) $1,200 is received at the beginning of year 1, $2,200 is received at the beginning of year 2, and $3,300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________. A) $ 6,700 B) $17,072 C) $12,510 D) $ 8,142
: D
20) Alexis owns stock in a company which has consistently paid a growing dividend over the last 10 years. The first year Alexis owned the stock, she received $4.50 per share and in the 10th year, she received $4.92 per share. What is the growth rate of the dividends over the last 10 years? A) 15 percent B) 14.8 percent C) 12.2 percent D) 9.3 percent
: D
23) To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year? A) $16,000 B) $17,920 C) $24,600 D) $27,552
: D
26) 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? A) $ 8,333 B) $13,572 C) $25,005 D) $22,109
: D
29) Zheng Sen wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years. If Zheng Sen can earn 10 percent on his investments, how much must he deposit at the end of each year? A) $ 14,900 B) $ 50,000 C) $117,453 D) $ 17,460
: D
33) Thelma is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year degree, assuming th expenses incur only at the end of the year. How much must Thelma deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college? A) $20,000 B) $13,620 C) $39,520 D) $11,270
: D
37) Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in three equal annual installments. The interest paid in the third year is ________. A) $277.95 B) $405.00 C) $352.00 D) $147.00
: D
41) How long would it take for you to save an adequate amount for retirement if you deposit $40,000 per year into an account beginning today that pays 12 percent per year if you wish to have a total of $1,000,000 at retirement? A) 12.2 years B) 10.5 years C) 14.8 years D) 11.5 years
: D
46) What effective annual rate of return (EAR) would Rayne need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years? A) 5.98% B) 6.55% C) 4.87% D) 6.14%
: D
7) Find the present value of the following stream of a firm's cash flows, assuming that the firm's opportunity cost is 14 percent. A) $121,256 B) $ 69,000 C) $ 60,513 D) $ 51,903
: D
9) Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? A) $19,292 B) $14,938 C) $40,000 D) $144,104
: D
9) Find the present value of the following stream of a firm's cash flows, assuming that the firm's opportunity cost is 9 percent. A) $ 13,252 B) $141,588 C) $ 10,972 D) $ 79,345
: D
1) Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the timing of cash flows does not have any significant economic consequences.
: FALSE
2) An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.
: FALSE
2) Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.
: FALSE
2) In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment declines over the life of the loan, and the interest portion of each payment grows over the life of the loan.
: FALSE
2) Time value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.
: FALSE
3) In general, with an amortized loan, the payment amount remains constant over the life of the loan, both the principal portion of and the interest portion declines over the life of the loan.
: FALSE
3) The greater the interest rate and the longer the period of time, the higher the present value.
: FALSE
4) In general, with an amortized loan, the payment amount grows over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion declines over the life of the loan.
: FALSE
5.5 Understand the effect that compounding interest more frequently than annually has on future value and on the effective annual rate of interest. 1) The nominal (stated) annual rate is the rate of interest actually paid or earned.
: FALSE
6) Everything else being equal, the higher the discount rate, the higher the present value.
: FALSE
6) The effective rate of interest is the contractual rate of interest charged by a lender or promised by a borrower.
: FALSE
6) When computing an interest or growth rate, the rate will decrease with an increase in future value, holding present value and the number of periods constant.
: FALSE
7) When computing an interest or growth rate, the rate will increase with a decrease in future value, holding present value and the number of periods constant.
: FALSE
8) For any interest rate and for any period of time, the more frequently interest is compounded, the greater the amount of money that has to be invested today in order to accumulate a given future amount.
: FALSE
9) The effective rate of interest and compounding frequency are inversely related.
: FALSE
9) When computing the number of deposits needed to accumulate a future sum, it will take longer if the interest rates are higher, holding the future value and deposit size constant.
: FALSE
20) China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000. If the growth rate in sales is projected to be 10 percent over the next five years, what will the dollar amount of sales be in year five?
: FV = 1,000,000(1.1)5 = $1,610,510
21) Calculate the future value of $10,000 received today and deposited for six years in an account which pays interest of 12 percent compounded quarterly.
: FV = 10,000{[(1.12/4)6×4 - 1]/.12/4} = 10,000{[(1.03)24 - 1]/.03} = $20,328
15) Calculate the combined future value at the end of year 3 of $1,000 received at the end of year 1, $3,000 received at the end of year 2, and $5,000 received at the end of year 3, all sums deposited at 5 percent.
: FV = 1000(1.05)2 + 3000(1.05) + 5000 = $9,252
19) Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually. She plans to leave the funds in this account for seven years earning interest. If the goal of this deposit is to cover a future obligation of $65,000, what recommendation would you make to Aunt Tillie?
: FV = 33,000(1.1)7 = $64,308 Aunt Tillie will only have $64,308 at the end of seven years under the stated arrangement. She must find an account with a higher interest rate or deposit a larger sum today. The amount Aunt Tillie should invest today to receive $65,000 after 7 years, PV = 65,000 / (1.1)7 = $33,355.28
68) Suzy wants to buy a house but does not want to get a loan. The average price of her dream house is $500,000 and its price is growing at 5 percent per year. How much should Suzy invest in a project at the end of each year for the next 5 years in order to accumulate enough money to buy her dream house with cash at the end of the fifth year? Assume the project pays 12 percent rate of return.
: FV = 500,000(1.05)5 = $638,141 PV = 0, I = 12, N = 5, FV = 638,141, CPT PMT = $100,450
20) Calculate the future value of $6,490 received today and deposited for five years in an account which pays interest of 14 percent compounded semiannually.
: FV = 6,490{[(1.14/2)5×2 - 1]/.14/2} = 6,490{[(1.07)10 - 1]/.07} = $12,766
27) Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6 percent.
: FV = CF[(1 + r)n - 1] / r = $5,000[(1.06)8 - 1] / 0.06 = $49,487.34
17) Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years.
: FV = PV (1+ r)n = $4,600(1.09)3 = $5,957
53) A firm wishes to establish a fund which, in 10 years, will accumulate to $10,000,000. The fund will be used to repay an outstanding bond issue. The firm plans to make deposits, which will earn 12 percent, to this fund at the end of each of the 10 years prior to maturity of the bond. How large must these deposits be to accumulate to $10,000,000?
: Financial Calculator: PV = 0, FV = 10000000, N = 10, I = 12, CPT PMT: $569,833.04
63) Herbert has opened a retirement fund account which pays 7 percent interest and requires $5,000 annual deposits. Herbert will retire in 15 years and expects 10 years of retirement life. What is the maximum annual retirement benefit Herbert can get during his retirement years?
: I = 7%, PMT = $5,000, N = 15, PV = 0 At the beginning of retirement: CPT FV = $125,645 Annual retirement benefit: i = 7%, n = 10, PV = $125,645, FV = 0 CPT PMT = $17,887.96
16) You are considering the purchase of new equipment for your company and you have narrowed down the possibilities to two models which perform equally well. However, the method of paying for the two models is different. Model A requires $5,000 per year payment for the next five years. Model B requires the following payment schedule. Which model should you buy if your opportunity cost is 8 percent?
: Model A: PV = (CF/i) × [1-1/(1+r)n] = (5,000/.08) × [1-1/(1.08)5] = $19,963.55 Buy Model A.
33) Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)
: P = ($1,000,000/0.1) × [1-(1/(1.1)20] = $8,514,000 $10,000,000 > $8,514,000 Accept the offer.
36) Nico is 30 years old and will retire at age 65. He will receive retirement benefits, but the benefits are not going to be enough to make a comfortable retirement life for him. Nico has estimated that an additional $25,000 a year over his retirement benefits will allow him to have a satisfactory life. How much should Nico deposit today in an account paying 6 percent interest to meet his goal? Assume Nico will have 15 years of retirement.
: PMT = $25,000, n = 15, r = 6% PV(65) = (25,000/.06) × [1-1/(1.06)15] = $242,806 FV = $242,806, n = 35, r = 6% P(30) = 242,800(1.06)-35 = 242,800(0.130) = $31,590
67) 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.
: PPV = 15000, I = 10, N = 2, FV = 0, CPT PMT = $3,444.32 The interest paid in the second year is $1,305.57.
22) Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent?
: PV = $70,000, r = 8%, n = 5 FV = 70,000(1.08)5 = $102,853.
18) Calculate the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 15 percent.
: PV = (12,000/.15) × [1-1/(1.15)7] + {(14,000/.15) × [1-1/(1.15)3]} × (1.15)-7 = $61,942
28) Calculate the present value of an annuity of $3,900 each year for four years, assuming an opportunity cost of 10 percent.
: PV = (3,900/0.1)[1-(1/(1.1)4)] = $12,363
26) Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.
: PV = 10,000/0.06 = $166,667
49) Marc has purchased a new car for $15,000. He paid $2,500 as down payment and he paid the balance by a loan from his hometown bank. The loan is to be paid on a monthly basis for two years charging 12 percent interest. How much are the monthly payments?
: PV = 15,000 - 2,500 = $12,500, r = 12%, n = 2, m = 12 Use financial calculator: PV = 12500, I = 1, n = 24, FV = 0, CPT PMT: $588.42
66) To expand its operation, International Tools Inc. has applied to the International Bank for a 3-year, $3,500,000 loan. Prepare a loan amortization table assuming 10 percent rate of interest.
: PV = 3500000, I = 10, N = 3, FV = 0, CPT PMT = $1,407,401.81
29) Dottie has decided to set up an account that will pay her granddaughter (Lexi) $5,000 a year indefinitely. How much should Dottie deposit in an account paying 8 percent annual interest?
: PV = 5,000/0.08 = $62,500
13) Calculate the present value of $5,800 received at the end of year 1, $6,400 received at the end of year 2, and $8,700 at the end of year 3, assuming an opportunity cost of 13 percent.
: PV = 5,800(1.13)-1 + 6,400(1.13)-2 + 8,700(1.13)-3 = $16,174.42
64) Brian borrows $5,000 from a bank at 8 percent annually compounded interest to be repaid in five annual installments. Calculate the principal paid in the third year.
: PV = 5000, I = 8, N = 3, FV = 0, CPT PMT = $1,252.19 The principal paid in the third year is $993.99.
14) Calculate the present value of $800 received at the beginning of year 1, $400 received at the beginning of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost of 9 percent.
: PV = 800 + 400(1.09) + 700(1.09)2 = $1,756.15
18) Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity cost of 14 percent.
: PV = 89,000(1.14)-15 = $12,469
34) Mr. Jackson has been awarded a bonus for his outstanding work. His employer offers him a choice of a lump-sum of $5,000 today, or an annuity of $1,250 a year for the next five years. Which option should Mr. Jackson choose if his opportunity cost is 9 percent?
: PVA = ($1,250/0.09) × [1-1/(1.09)5] = $4,862.06 Mr. Jackson should choose a lump-sum of $5,000 today.
31) Nico establishes a seven-year, 8 percent loan with a bank requiring annual end-of-year payments of $960.43. Calculate the original principal amount.
: PVA = (960.43/0.08)[1-(1/(1.08)7)] = $5,000
65) Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a sports car from her friend, Jim. She has $2,500 now and would like to save equal annual end-of-year deposits to pay for the car. How much should she deposit at the end of each year in an account paying 8 percent interest to buy the car?
: Using financial calculator: PV = -2500, N = 3, I = 8, FV = 10000, CPT PMT = 2110.25
37) You have been given a choice between two retirement policies as described below. Policy A: You will receive equal annual payments of $10,000 beginning 35 years from now for 10 years. Policy B: You will receive one lump-sum of $100,000 in 40 years from now. Which policy would you choose? Assume rate of interest is 6 percent.
: Policy A: present value of the annuity at the beginning of the 35 years from now: PVA = (10,000/0.06) × [1-1/(1.06)10] = $73,600 Policy B: present value of the lump-sum at the beginning of the 35 years from now: PV = 100,000(1.06)-5 = $74,726 I will choose policy B.
1) For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.
: TRUE
1) In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion of each payment declines over the life of the loan.
: TRUE
2) The nominal and effective rates are equivalent for annual compounding.
: TRUE
3) The effective annual rate increases with increasing compounding frequency.
: TRUE
3) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero.
: TRUE
4) Everything else being equal, the higher the interest rate, the higher the future value.
: TRUE
4) The annual percentage rate (APR) is the nominal rate of interest, found by multiplying the periodic rate by the number of periods in one year.
: TRUE
5) Future value increases with increases in the interest rate or the period of time funds are left on deposit.
: TRUE
5) The annual percentage yield (APY) is the effective rate of interest that must be disclosed to customers by banks on their savings products as a result of "truth in savings laws."
: TRUE
5) When computing an interest or growth rate, the rate will increase with an increase in future value, holding present value and the number of periods constant.
: TRUE
5.3 Find the future value and the present value of both an ordinary annuity and an annuity due, and find the present value of a perpetuity. 1) An annuity due is an amount that occur at the beginning of each period.
: TRUE
7) Everything else being equal, the longer the period of time, the lower the present value.
: TRUE
7) The effective rate of interest differs from the nominal rate of interest in that it reflects the impact of compounding frequency.
: TRUE
8) When computing the number of deposits needed to accumulate to a future sum, it will take longer if the interest rate decreases, holding the future value and deposit size constant.
: TRUE
23) Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)
: The PV of X = $1,000,000; The PV of Y = $1,371,000; The FV of X = $1,276,000; The FV of Y = $1,500,000. Based on both present values and future values, B is the better choice. Finding present values and future values are simply reverse processes of one another, and that choosing between two lump sums based on PV will always give the same result as choosing between the same two lump sums based on FV.
35) In their meeting with their advisor, Mr. and Mrs. O'Rourke concluded that they would need $40,000 per year during their retirement years in order to live comfortably. They will retire 10 years from now and expect a 20-year retirement period. How much should Mr. and Mrs. O'Rourke deposit now in a bank account paying 9 percent to reach financial happiness during retirement?
: The amount of money required at the beginning of the retirement period is: n = 20, i = 9% PVA = (CF/r) × [1-1/(1+r)n] = (40,000/.09) × [1-1/(1.09)20]= $365,142 n = 10, i = 9% PV = 365,142(1.09)-10 = $154,239.85
50) You have been given the opportunity to earn $20,000 five years from now if you invest $9,524 today. What will be the rate of return to your investment?
: Use financial calculator: PV = -9524, FV = 20000, PMT = 0, N = 5, CPT I: 16%
47) Janice borrows $25,000 from the bank at 15 percent to be repaid in 10 equal annual installments. Calculate the end-of-year payment.
: Use financial calculator: PV = 25,000, I = 15, FV = 0, N = 10, CPT PMT: $4,981.30
55) The New York Soccer Association would like to accumulate $10,000 by the end of 4 years from now to finance a big soccer weekend for its members. The Association currently has $2,500 and wishes to raise the balance by arranging annual fund-raising events. How much money should they raise at each annual fund-raising event assuming 8 percent rate of interest?
: Using Financial Calculator: PV = -2500, FV = 10000, N = 4, I = 8, CPT PMT: 1464.41
54) John borrowed $12,000 to buy a new car and expects to pay $564.87 per month for the next 2 years to pay off the loan. What is the loan's rate of interest?
: Using Financial Calculator: PV = 12000, FV = 0, N = 24, PMT = -564.87, CPT I: 0.9998 × 12 = 12%
51) Ten years ago, Tom purchased a painting for $300. The painting is now worth $1,020. Tom could have deposited $300 in a savings account paying 12 percent interest compounded annually. Which of these two options would have provided Tom with a higher return?
: Using financial calculator: PV = - $300, FV = $1,020, n = 10, PMT = 0, CPT I: 13% Painting has a higher return (13 percent) in comparison to the 12 percent rate of return from the savings account.
57) A deep-discount bond can be purchased for $312 and in 20 years it will be worth $1,000. What is the rate of interest on the bond?
: Using financial calculator: PV = -312, PMT = 0, N = 20, FV = 1000, CPT I = 6 percent
61) To buy his favorite car, Larry is planning to accumulate money by investing his Christmas bonuses for the next five years in a security which pays a 10 percent annual rate of return. The car will cost $20,000 at the end of the fifth year and Larry's Christmas bonus is $3,000 a year. Will Larry accumulate enough money to buy the car?
: Using financial calculator: PV = 0, N = 5, PMT = 3000, I = 10, CPT FV = $18,315 Larry will not have enough money to buy the car. He should either invest more money or deposit his christmas bonuses in a security paying a higher rate of return.
52) Find the equal annual end-of-year payment on $50,000, 15 year, and 10 percent loan.
: Using financial calculator: PV = 50,000, FV = 0, N = 15, I = 10, CMP PMT: $6,573.69
58) Timothy borrows $6,930 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $2,281.86. Calculate the interest rate on the loan.
: Using financial calculator: PV = 6930, PMT = -2281.86, N = 4, FV = 0, CPT I = 12%
62) Mr. & Mrs. Pribel wish to purchase a boat in 8 years when they retire. They are planning to purchase the boat using proceeds from the sale of their property which is currently worth $90,000 and its value is growing at 7 percent a year. The boat is currently worth $200,000 increasing at 5 percent per year. In addition to the value of their property, how much additional money should they deposit at the end of each year in an account paying 9 percent annual interest in order to be able to buy the boat upon retirement?
: Value of the property upon retirement: PV = $90,000, I = 7, N = 8, PMT = 0 CPT FV = $154,637 Value of the boat upon retirement: PV = $200,000, I = 5, N = 8, PMT = 0 CPT FV = $295,491 Additional money needed upon retirement: $295,491 - $154,637 = $140854 Amount of money needed to deposit at the end of each year: PV = 0, FV = $140,780, N = 8, I = 9%, PMT = ? PMT = $12,765.69
48) The following table presents the Sally's Silly Service Company's net earnings for the past six years. Compute the growth rate in the company's earnings.
: g = (FV/PV)1/n - 1, n = 5, FV = 2659, PV = 1728 g = (2659/1728)1/5 - 1 = .09 = 9%
21) Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing $7,000, two years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semiannually?
: n = 2, m = 2, r = 8% FV = 6,000(1+.08/2)2 × 2 = 6000(1.04)4 = $7,019 Yes, Colin will have enough money to buy the scooter.
