FINC 409 Chapter 9
You want to buy a Volvo in seven years. The car is currently selling for $50,000, and the price will increase at a compound rate of 10% per year. You can presently invest in high-yield bonds earning a compound annual rate 14% per year. How much must you invest at the end of each of the next seven years to be able to purchase your dream car in seven years? Pick the closest answer. a. $8,831.46 b. $9,080.20 c. $9,125.42 d. $9,282.09
b. $9,080.20 PV 50,000 N 7 I/Y 10 → FV = $97,435.86 cost of car 7 years from today END mode PV 0 FV 97,435.86 N 7 I/Y 14 → PMT = $9,080.28
If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the APR is: Pick the closest answer. a. 10.38% b. 10.00% c. 2.50% d. 39.06%
b. 10.00% APR = 2.5% × 4 = 10%
Shelby was given a gold coin originally purchased for $1 by her 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: Pick the closest answer. a. 12% b. 13% c. 14% d. cannot be determined with the given information
b. 13% PV -1 FV 450 N 50 → I/Y = 13%
Megan owns stock in a company which has consistently paid a growing dividend over the last five years. At the end of the first year Megan 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 during this time? Pick the closest answer. a. 11 percent b. 14 percent c. 12 percent d. 13 percent
b. 14 percent PV -1.71 FV 2.89 N 4 → I/Y = 14.02%
If you have an account with a 21.5% annual percentage rate where interest is compounded quarterly, what is the effective annual rate of interest? Pick the closest answer. a. 23.75% b. 23.3% c. 21.5% d. 5.375%
b. 23.3% interest per quarter=21.5/4=5.375%→EAR=(1+0.05375)^4-1=1.23296-1=23.3%
In 1976, the average price of a domestic car was $5,100. Twenty years later, in 1996, the average price was $16,600. What was the annual growth rate in the car price over the 20-year period? Pick the closest answer. a. 5.89% b. 6.07% c. 7.12% d. 8.23%
b. 6.07% PV 5,100 FV -16,600 N 20 → I/Y = 6.07%
In 1983, the average tuition for one year in the MBA program at a university was $3,600. Thirty years later, in 2013, the average tuition was $27,400. What is the compound annual growth rate in tuition (rounded to the nearest whole percentage) over the 30-year period? Pick the closest answer. a. 6% b. 7% c. 8% d. 10%
b. 7% PV 3,600 FV -27,400 N 30 → I/Y = 7.0%
Larry deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective interest rate? a. 8.00% b. 8.24% c. 8.33% d. 8.46%
b. 8.24% r is the interest charged per period → 8% compounded quarterly is 2% per quarter EAR = (1 + r)m - 1 = (1.02)4 - 1 = 8.24%
Your current bank is paying 6.25% simple interest rate. You can move your savings account to Harris Bank that pays 6.25% compounded annually or to First Chicago bank paying 6% compounded semi-annually. To maximize your return you would choose: a. your current bank (not as good as annual compounding in Harris Bank) b. Harris Bank (EAR = 6.25%) c. First Chicago bank (6% semi-annually → 6% ÷ 2 = 3% every 6 months (semi-annual)) d. you are indifferent, because the effective interest rate for all three banks is the same (EAR = (1 + .03)2 - 1 = 1.0609 - 1 = 6.09%)
b. Harris Bank (EAR = 6.25%)
Which of the following characteristics is not descriptive of an amortization schedule? a. Each payment is the same. b. The same dollar amount of interest is paid with each payment. the dollar amount decreases c. Payment on principal increases with each total payment. d. Balance owed is reduced by the principal portion of each payment.
b. The same dollar amount of interest is paid with each payment. the dollar amount decreases
A loan that is repaid in equal payments over a specified time period is referred to as a(n): a. discounted loan b. amortized loan c. simple interest-free loan d. inflation-indexed loan
b. amortized loan
When the amount earned on a deposit becomes part of the principal at the end of a period and can earn a return in future periods, this is called a. discount interest. b. compound interest. c. primaryinterest. d. future value.
b. compound interest.
If the stated or nominal interest rate is 10 percent and the inflation rate is 4 percent, the net or differential compounding rate would be ________ percent a. ten b. six c. four d. fourteen
b. six 10% - 4% = 6%
Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years. One is an annuity due, while the other is an ordinary annuity. Which annuity should you choose? a. the ordinary annuity b. the annuity due c. either one because the annuities have the same present value d. without information about the appropriate interest rate, we cannot tell which annuity is better
b. the annuity due with the annuity due payments are received sooner → worth more today
Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The amount paid toward the principal in the first year's payment is: Pick the closest answer. a. $1,155 b. $2,481.91 c. $1,326.91 d. $8,018.90
c. $1,326.91 annual payment: END mode PV 10,500 N 6 I/Y 11 FV 0 → PMT = - $2,481.91 interest part of 1ST payment: 10,500(0.11) = $1,155 principal part of 1ST payment: 2,481.91 - 1,155 = $1,326.91
Olivia borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is: Pick the closest answer. a. $1,323 b. $1,298 c. $1,482 d. $1,518
c. $1,482 END mode PV 4,500 FV 0 N 4 I/Y 12 → PMT = -$1,481.55
A wealthy inventor has decided to endow her favorite art museum by establishing funds for an endowment which would provide $1,000,000 per year forever. She will fund 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 5 percent in all future periods. How much must the scientist deposit each year to accumulate to the required amount? Pick the closest answer. a. $1,875,333 b. $736,000 c. $1,590,091 d. $943,396
c. $1,590,091 (ENDOWMENT)(0.05)=1,000,000→ Endowment=1,000,000/0.05=$20,000,000 END mode FV 20,000,000 PV 0 N 10 I/Y 5 → PMT = -$1,590,091
Assume a lender offers you a $25,000, 10%, three-year loan that is to be fully amortized with three annual payments. The first payment will be due one year from the loan date. How much will you have to pay each year? Pick the closest answer. a. $8,042 b. $9,026 c. $10,053 d. $11,120
c. $10,053 END mode PV 25,000 FV 0 N 3 I/Y 10 → PMT = $10,052.87
A hospital received a contribution to its endowment fund of $2 million. The hospital can never touch the principal, but it can use the earnings. At an assumed interest rate of 9.5 percent, how much can the hospital earn to help its operations each year? Pick the closest answer. a. $95,000 b. $19,000. c. $190,000. d. $18,000.
c. $190,000. $2,000,000(0.095) = $190,000
You put $2,000 in an IRA account at Northern Trust. This account pays a fixed interest rate of 8% compounded quarterly. How much money do you have in five years? Pick the closest answer. a. $2,914 b. $2,939 c. $2,972 d. $2,999
c. $2,972 PV 2,000 N 20 I/Y 2 → FV = $2,971.89
Kristen plans to start her college education four years from now. To pay for her college education, she has decided to save $1,000 at the end of each 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? Pick the closest answer. a. $20,762 b. $5,353 c. $20,157 d. $4,779
c. $20,157 END mode PMT -1,000 N 16 I/Y 3 PV 0 → FV = $20,156.88
An ordinary annuity of $5,000 invested at 8% in 5 years would result in a future value of (Pick the closest answer.): a. $25,000 b. $7,345 c. $29,333 d. $31,680
c. $29,333 END mode PMT -5,000 PV 0 N 5 I/Y 8 → FV = $29,333.00
Suppose you were going to save $1,000 per year for three years at a 10% interest rate compounded annually, with the first investment occurring today. What would be the future value of this investment? Pick the closest answer. a. $2,124 b. $2,310 c. $3,641 d. $3,812
c. $3,641 BGN mode PMT -1,000 N 3 I/Y 10 PV 0 → FV = $3,641
You borrow $10,000 to pay for your college tuition.The loan is amortized over a 3 year period with an interest rate 18%. The payments are made at the end of each year. What is your remaining balance at the end of year two? Pick the closest answer. a. $7,201 b. $4,599 c. $3,898 d. $3,303
c. $3,898 END mode PV 10,000 FV 0 I/Y 18 N 3 → PMT = $4,599.24 YR1: INT = 18%(10,000) = $1,800 → PRIN = 4,599.24 - 1,800 = $2,799.24 END BAL = 10,000 - 2,799.24 = $7,200.76 YR2: INT = 7,200.76(0.18) = $1,296.14 → PRIN 4,599.24 - 1,296.14 = $3,303.10 END BAL 7,200.76 - 3,303.10 = $3,897.66
Collin 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 Collin can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer. a. $22,000 b. $20,000 c. $31,875 d. $35,062
c. $31,875 END mode PV 0 PMT -2,000 N 10 I/Y 10 → FV = $31,874.85
$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 ________. Pick the closest answer. a. $1,536.25 b. $672.86 c. $727. 37 d. $1,245.16
c. $727. 37 1ST DEPOSIT: PV 100 N 3 I/Y 12 → FV = $140.49 2ND DEPOSIT: PV 200 N2 I/Y 12 → FV = $250.88 3RD DEPOSIT: PV 300 N 1 I/Y 12 → FV = $336.00 TOTAL $727.37
Taylor has just accepted a job as a stockbroker. He estimates his gross pay each year for the next three years is $35,000 in year 1, $21,000 in year 2, and $32,000 in year 3. His gross pay is received at the end of each year. Calculate the present value of these cash flows, if they are discounted at 4%. Pick the closest answer. a. $79,452.30 b. $80,294.50 c. $81,517.10 d. $88,000
c. $81,517.10 FV 35,000 N 1 I/Y 4 → PV = $33,653.85 FV 21,000 N 2 I/Y 4 → PV = $19,415.68 FV 32,000 N 3 I/Y 4 → PV = $28,447.88 $81,517.10
When solving for the future value of an amount deposited now, which one of the following factors would not be part of the calculation? a. present value amount b. 1 plus the interest rate c. 1 divided by the sum of 1 plus the interest rate d. number of periods to compound over
c. 1 divided by the sum of 1 plus the interest rate
If the APR is 12% and interest is compounded monthly, then the EAR is: Pick the closest answer. a. 12.00% b. 1.00% c. 12.68% d. none of the above
c. 12.68% monthly interest rate=12%/12=1% EAR= (1+1%)^12-1=1.1268-1= 12.68%
What is the highest effective rate attainable with a 12 percent nominal rate? Pick the closest answer. a. 12.00% b. 12.55% c. 12.72% d. 12.95%
c. 12.72% DAILY: (1+12/365)^365-1 = (1.0003288)^365-1 = 12.72%
You deposit $1,000 in a long-term certificate of deposit with an interest rate of 8.81%. How many years will it take for you to triple your deposit? Pick the closest answer. a. 11 years b. 12 years c. 13 years d. 14 years
c. 13 years PV -1,000 FV 3,000 I/Y 8.81 → N = 13.01
Consolidated Freightways is financing a new truck with a loan of $60,000 to be repaid in six annual end-of- year installments of $13,375. What annual interest rate is Consolidated Freightways paying? Pick the closest answer. a. 7% b. 8% c. 9% d. 10%
c. 9% END mode PV 60,000 PMT -13,375 N 6 FV 0 → I/Y = 9%
Which of the following statements is false? a. For a given APR, more frequent compounding results in additional return on the investment. b. An amortized loan is repaid in equal payments over a specified time period. c. The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year. d. Each of the above statements is true.
c. The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year.
A loan that is repaid in equal payments over a specified time period is called a(n): a. discount loan b. balloon loan c. amortized loan d. none of the above
c. amortized loan
A series of equal payments or receipts that occur at the beginning of each of a number of time periods is referred to as: a. an ordinary annuity b. a deferred annuity c. an annuity due d. an extraordinary annuity
c. an annuity due
The method of calculating interest on a loan that is set by law is called the: a. negotiated legal rate (NLR) b. effective annual rate (EAR) c. annual percentage rate (APR) d. none of the above
c. annual percentage rate (APR)
The future value of a dollar ________ as the interest rate increases and ________ the farther in the future the funds are to be received. a. decreases; decreases. b. decreases; increases. c. increases; increases. d. increases; decreases.
c. increases; increases.
Which of the following terms best describes an annuity due? a. decreasing payments b. increasing payments c. payment at beginning of year d. payment at the end of the year
c. payment at beginning of year
A famous athlete is awarded a contract that stipulates equal payments to be made monthly over a period of five years. To determine the value of the contract today, you would need to use: a. present value of a single lump sum b. future value of a single lump sum c. present value of an annuity d. future value of an annuity
c. present value of an annuity annuity ≡ series of equal payments (receipts) that occur over a number of time periods
What would be the future value of a CD of $1,000 for two years if the bank offered a 10% interest rate compounded semiannually? Pick the closest answer. a. $1,720 b. $1,960 c. $1,200 d. $1,216
d. $1,216 PV 1,000 N 4 I/Y 5 → FV = $1,215.51
The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is: Pick the closest answer. a. $1,303.14 b. $1,241.02 c. $1,620.46 d. $1,558.14
d. $1,558.14 use the opportunity cost of 4% as the discount rate END mode PMT -350 N 5 I/Y 4 FV 0 → PV = $1,558.14
Megan is planning for her son's college education to begin five years from today. Megan estimates the yearly tuition to be $5,000 per year for a four-year degree. Tuition must be paid at the beginning of each year. How much must Megan 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? Pick the closest answer. a. $20,000 b. $13,620 c. $39,520 d. $12,173
d. $12,173 tuition paid BGN each year → money needed at BGN of the first year of college: BGN mode PMT -5,000 N 4 1/Y 8 FV 0 → PV = $17,885.48 deposit needed today: FV 17,885.48 N 5 I/Y 8 → PV = $12,172.56 OR money needed today for: 1st TUITION: FV 5,000 N 5 I/Y 8 → PV = $3,402.92 2ND TUITION: FV 5,000 N 6 I/Y 8 → PV = $3,150.85 3RD TUITION: FV 5,000 N 7 I/Y 8 → PV = $2,917.45 4TH TUITION: FV 5,000 N 8 I/Y 8 → PV = $2,701.34 TOTAL $12,172.56
Lance 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 he can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? Pick the closest answer. a. $44,800 b. $161,397 c. $40,000 d. $144,105
d. $144,105 END mode PV 0 PMT -2,000 N 20 I/Y 12 → FV = $144,104.88
Jonathan wishes to accumulate $1 million by making equal annual end-of-year deposits over the next 20 years. If he can earn 10 percent on his investments, how much must he deposit at the end of each year? Pick the closest answer. a. $15,872 b. $50,000 c. $16,643 d. $17,460
d. $17,460 END mode FV 1,000,000 I/Y 10 N 20 PV 0 → PMT = -$17,459.62
A ski chalet in Vail now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Larry and his wife 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? Pick the closest answer. a. $23,333 b. $19,565 c. $24,005 d. $22,108
d. $22,108 PV 250,000 N 10 I/Y 5 → FV = $407,223.66 END mode FV 407,223.66 N 10 I/Y 13 PV 0 → PMT = -$22,107.99
Lance deposits $2,000 per year at the end of the year for the next 15 years into an IRA account that currently pays 7%. How much will Lance have on deposit at the end of the 15 years? Pick the closest answer. a. $39,981 b. $46,753 c. $49,002 d. $50,258
d. $50,258 END mode PMT -2,000 N 15 I/Y 7 PV 0 → FV = $50,258.04
Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The loan balance at the end of the first year is: Pick the closest answer. a. $8,934.24 b. $9,345 c. $8,018.91 d. $9,173.09
d. $9,173.09 annual payment: END mode PV 10,500 N 6 I/Y 11 FV 0 → PMT = - $2,481.91 interest part of 1ST payment: 10,500(0.11) = $1,155 principal part of 1ST payment: 2,481.91 - 1,155 = $1,326.91 loan balance end of 1st year: 10,500 - 1,326.91 = $9,173.09
Taylor owns stock in a company which has consistently paid a growing dividend over the last 10 years. At the end of the first year Taylor owned the stock, he received $4.50 per share and at the end of the 10th year, he received $4.92 per share. What is the growth rate of the dividends during this time? Pick the closest answer. a. 3% b. 4% c. 2% d. 1%
d. 1% PV -4.50 FV 4.92 N 9 → I/Y = 1%
Which of the following statements is false? a. The present value of a future sum decreases as the discount rate increases. b. If the present value of a sum is equal to its future value, the interest rate must be zero. c. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. d. For a given APR, the present value of a future sum decreases as the number of discounting periods per year decreases.
d. For a given APR, the present value of a future sum decreases as the number of discounting periods per year decreases. you would need to deposit more today if there a fewer compounding (discounting) periods
The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate
d. effective annual rate
When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the: a. annual percentage rate b. contract rate c. stated rate d. effective annual rate
d. effective annual rate
The basic future and present value equations contain four variables. Which one of the following is not included? a. present value (PV) b. future value (FV) c. interest rate (r) d. inflation rate (I) e. number of periods (n)
d. inflation rate (I)
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. present value of an annuity using the amount of the loan as PV → calculate the PMT
An annuity due may also be referred to as a deferred annuity.
false
As the number of periods increases, present value increases.
false
Because interest compounds, the annual percentage rate formula will overstate the true interest cost of a loan.
false
For a given discount rate, an ordinary annuity and an annuity due have the same present value.
false
The annual percentage rate (APR) overstates the true or effective interest cost.
false
The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year.
false
With compound interest, interest is earned only on the investment's principal.
false
The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 15%.
false END mode PMT -100 FV 1,593.74 N 10 PV 0 → I/Y = 10%
The present value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.
false END mode PMT 100 N 10 I/Y 10 FV 0 → PV = $614.46
The future value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46.
false END mode PV 0 PMT 100 N 10 I/Y 10 → FV = $1,593.74
The present value of a $100 received in 10 years at 10% is $259.37.
false FV 100 N 10 I/Y 10 → PV = $38.55
It will take approximately 9.6 years for a $100 deposit to result in a future value of $600 if I can earn 10% on my deposit.
false PV -100 FV 600 I/Y 10 → N = 18.8 years
If I earn 3% on my deposit of $500, it will take 9 years before I have $550.
false PV -500 FV 550 I/Y 3 → N = 3.22 years
The future value of $100 deposited today for 10 years at 10% compounded annually is $38.55.
false PV 100 N 10 I/Y 10 → FV = $259.37
The interest portion increases and the principal portion decreases over time under a typical loan amortization schedule.
false decreases, increases
The annual percentage rate is the true opportunity cost measure of the interest rate.
false effective annual rate
If the interest rate is 0% for 10 years, then the present value will be less than the future value.
false it will be the same
Level cash flow amounts that occur at the end of each period, starting at the end of the first period, are an annuity due.
false ordinary annuity
An ordinary annuity exists when the equal payments occur at the beginning of each time period.
false ordinary annuity payments occur at the end of each time period
At very high interest rates the "Rule of 72" will result in a small estimation error for the estimate of the time for an investment to double.
false same is true at very low interest rates
Simple interest is interest earned on the investment's principal and subsequently-earned interest.
false simple interest does not earn interest on previously earned interest
A fixed-rate mortgage is an example of an annuity.
true
A loan amortization schedule shows the breakdown of each payment between interest and principal, as well as the remaining balance after each payment.
true
An amortized loan is repaid in equal payments over a specified time period.
true
An annuity is a series of equal payments that occur over a number of time periods.
true
As the interest rate increases, present value decreases.
true
At a zero interest rate, the present value of $1 remains at $1 and is not affected by time.
true
Compound interest is interest earned on interest in addition to interest earned on the principal.
true
Compounding means that interest earned each year, plus the principal, will be reinvested at the stated rate.
true
Discounting is an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value.
true
For the same annual percentage rate, more frequent compounding increases the future value of an investor's funds more quickly.
true
Money has a time value so long as interest is earned by saving or investing money.
true
The Rule of 72 is an estimate of how long it would take to double a sum of money at a given interest rate.
true
The effective annual rate (EAR) is sometimes called the annual effective yield.
true
The effective annual rate (EAR) is the true opportunity cost measure of the interest rate.
true As compared to the Annual Percentage Rate (APR)
The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 10%.
true END mode PMT -100 FV 1,593.74 N 10 PV 0 → I/Y = 10%
The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $614.46 is negative 11.45%.
true END mode PMT -100 N 10 FV 614.46 PV 0 → I/Y = -11.45%, this is a negative % because you end up with $614.46 which is less than your ten deposits = 10($100) = $1,000
The present value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46.
true END mode PMT 100 N 10 I/Y 10 FV 0 → PV = $614.46
The future value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74.
true END mode PV 0 PMT 100 N 10 I/Y 10 → FV = $1,593.74
The present value of $100 received in 10 years at 10% compounded annually is $38.55
true FV 100 N 10 I/Y 10 → PV = $38.55
$1000 deposited in a bank that earns 7% per year will become approximately $7,600 in 30 years.
true PV -1,000 I/Y 7 N 30 → FV = $7,612.26
It will take approximately 18.8 years for a $100 deposit to grow to $600 if I can earn 10% on my deposit.
true PV -100 FV 600 I/Y 10 → N = 18.8 years
The return provided by $100 deposited today for 10 years that results in a future value of $614.46 is 19.91%.
true PV -100 N 10 FV 614.46 → I/Y = 19.91%
The future value of $100 deposited today for years at 10% compounded annually is $259.37.
true PV 100 N 10 I/Y 10 → FV = $259.37
The method of calculating the annual percentage rate (APR) is set by law.
true by the Truth in Lending law, APR = r×m, r=interest rate charged per period, m=number of periods, 1%/month → APR=12%
When the annual interest rate stays the same, more frequent interest compounding helps savers earn more interest over the course of the year.
true earn interest on the interest sooner → higher FV in future
If the compound inflation rate were greater than the compound interest rate, future purchasing power on our savings would fall.
true invest $100 today for 2 years at 4% compounded annually → FV = $108.16 if inflation for next 2 years is 7% compounded annually → what costs $100 will cost $114.49 in 2 years → your future savings won't buy what $100 would buy today, purchasing power fell
At very low interest rates, the "Rule of 72" does not approximate the compounding process well
true same is true at very high interest rates
Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The amount paid toward interest in the first year's payment is: Pick the closest answer. a. $1,155 b. $2,481 c. $144 d. $1,327
a. $1,155 10,500(0.11) = $1,155
If $1,000 were invested now at a 12% interest rate compounded annually, what would be the value of the investment in two years? Pick the closest answer. a. $1,254 b. $1,210 c. $1,188 d. $1,160
a. $1,254 PV 1,000 N 2 I/Y 12 → FV = $1,254.40
Assume that a borrower is willing to pay you $2,000 at the end of three years in return for a sum of money now. To receive a return of 10%, what is the most you should be willing to lend now? Pick the closest answer. a. $1,503 b. $1,786 c. $1,802 d. $1,818
a. $1,503 FV 2,000 N 3 I/Y 10 → PV = $1,502.63
The future value of $100 received today and deposited at 6 percent for four years is: Pick the closest answer. a. $126.25 b. $126.53 c. $141.85 d. $116.99
a. $126.25 PV -100 N 4 I/Y 6 → FV = $126.25
The future value of $200 received today and deposited for three years in an account which pays 8 percent interest compounded semiannually is ________. Pick the closest answer. a. $253.06 b. $251.94 c. $253.35 d. $212.27
a. $253.06 PV 200 N 6 I/Y 4 → FV = $253.06
The present value of an annuity of $5,000 to be received at the end of each of the 6 years at a discount rate of 4% would be: (Pick the closest answer.) a. $26,211 b. $33,165 c. $3,950 d. $27,259
a. $26,211 END mode PMT +5,000 FV 0 N 6 I/Y 4→ PV = -$26,210.68
Shannon plans to fund his individual retirement account (IRA) with the maximum contribution of $2,500 at the end of each year for the next 30 years. If Shannon can earn 10 percent on his contributions, how much will he have at the end of the tenth year? Pick the closest answer. a. $39,844 b. $411,235 c. $43,828 d. $27,500
a. $39,844 END mode PMT -2,500 N 10 I/Y 10 PV 0 → FV = $39,843.56
Tracey deposits $5,000 in a five-year certificate of deposit paying 6% compounded semi-annually. How much will Tracey have at the end of the five-year period? Pick the closest answer. a. $6,720 b. $6,690 c. $6,596 d. $6,910
a. $6,720 PV 5,000 I/Y 3 N 10 → FV = $6,719.58
Jonathan borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments, with the payments being made at the end of each year. The loan balance at the end of the second year is: Pick the closest answer. a. $7,700.17 b. $5,536.18 c. $8,164.05 d. $9,113.72
a. $7,700.17 annual payment: END mode PV 10,500 N 6 I/Y 11 FV 0 → PMT = - $2,481.91 interest part of 1ST payment: 10,500(0.11) = $1,155 principal part of 1ST payment: 2,481.91 - 1,155 = $1,326.91 loan balance end of 1st year: 10,500 - 1,326.91 = $9,173.09 interest part of 2ND payment: 9,173.09(0.11) = $1,009.04 principal part of 2ND payment: 2,481.91 - 1,009.04 = $1,472.87 loan balance end of 2ND year: 9,173.04 - 1,472.87 = $7,700.17
Claire bought 100 shares of Minnesota Mining and Manufacturing in June, 1987 for $38 a share for a total investment of $3,800. She sold the shares in June, 1996 for $8,960. What is Cecilia's annual rate of return on her investment? Pick the closest answer. a. 10% b. 10.6% c. 11% d. 11.2%
a. 10% PV 3,800 N 9 FV 8,960 → I/Y = 10%
If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the EAR is: Pick the closest answer. a. 10.38% b. 10.00% c. 2.50% d. 39.06%
a. 10.38% EAR = (1 + 2.5%)4 -1 = 1.1038 - 1 = 10.38%
Suppose you receive $3,000 a year in Years One through Four, $4,000 a year in Years Five through Nine, and $2,000 a year in Year Ten, with all the money to be received at the end of the year. If your discount rate is 12%, what is the present value of these cash flows? Pick the closest answer. a. 18,926.12 b. 19,560.80 c. 20,651.24 d. 24,175.00
a. 18,926.12 YR 1-4: END mode PMT 3,000 FV 0 N 4 I/Y 12 → PV0 = $9,112.05 YR 5-9: END mode PMT 4,000 FV 0 N 5 I/Y 12 → PV5 = $14,419.10 begin yr 5 BACK TO NOW: FV 14,419.10 N 4 I/Y 12 → PV0 = $9,163.60 YR 10: FV 2,000 N 10 I/Y 12 → PV0 = $643.95 TOTAL: 9,112.05 + 9,163.60 + 643.95 = $18,919.60
Your subscription to Consumer Reports is about to expire. You may renew it for $24 a year or, instead, you may get a lifetime subscription to the magazine for a onetime payment of $400 today. Payments for the regular subscription are made at the beginning of each year. Using a discount rate of 5%, how many years does it take to make the lifetime subscription the better deal? Pick the closest answer. a. 33 years b. 28 years c. 36 years d. 40 years
a. 33 years BGN mode PV 400 FV 0 PMT -24 I/Y 5 → N = 32.3 → 33 years Check: FV 0 PMT -24 I/Y 5 N 33 → PV = $403.26 FV 0 PMT -24 I/Y 5 N 32 → PV = $398.23
If a savings bond can be purchased today for $29.50 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond? Pick the closest answer. a. 5% b. 6% c. 7% d. 8%
a. 5% PV -29.50 FV 100 N 25 → I/Y = 5%
Your college has agreed to give you a $10,000 tuition loan. As part of the agreement, you must repay $12,600 at the end of the three-year period. What interest rate is the college charging? a. 8% b. 9% c. 11% d. 6%
a. 8% enter 10,000 as a positive number and 12,600 as a negative number PV 10,000 FV -12,600 N 3 → I/Y = 8%, single lump sum type of TVM problem
Assume your bank has a choice between two deposit accounts. Account A has an annual percentage rate of 4.62 percent with interest compounded monthly. Account B has an annual percentage rate of 4.62 percent but with interest compounded quarterly. 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. Account A when the annual stated rate is the same, more frequent compounding helps savers earn more interest over the course of a year (i.e. a higher EAR)
Assume your bank has a choice between two deposit accounts. Account A has an annual percentage rate of 7.55 percent with interest compounded monthly. Account B has an annual percentage rate of 7.45 percent with interest compounded monthly. Which account provides the highest effective annual return? a. Account A *EAR=(1+7.55/12)^12-1= (1+0.006292)^12-1= 1.07817-1=7.817%* b. Account B *EAR=(1+7.45/4)^4-1=(1+0.018625)^4-1= 1.07661-1=7.661* c. Both provide the same effective annual return. d. We don't have sufficient information to make a choice.
a. Account A *EAR=(1+7.55/12)^12-1= (1+0.006292)^12-1= 1.07817-1=7.817%*
The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the: a. annual percentage rate b. compound rate of interest c. stated rate of interest d. effective annual rate
a. annual percentage rate
In future value or present value problems, unless stated otherwise, cash flows are assumed to be a. at the end of a time period. b. at the beginning of a time period. c. in the middle of a time period. d. spread out evenly over a time period.
a. at the end of a time period.
The _________ value of a savings or investment is its amount or value at the current time. a. present b. future c. book d. none of the above
a. present
You need to have $35,000 on hand to buy a new Lexus five years from today. To achieve that goal, you want to know how much you must invest today in a certificate of deposit guaranteed to return you 3% per year. To help determine how much to investment today, you will use: a. present value of a single lump sum b. future value of a single lump sum c. present value of an annuity d. future value of an annuity
a. present value of a single lump sum the $35,000 you need 5 years from now is a single lump sum → use present value
Interest earned only on an investment's principal or original amount is referred to as: a. simple interest b. compound interest c. discount interest d. annuity interest
a. simple interest
Megan puts $1,000 in a savings passbook that pays 4% compounded quarterly. How much will she have in her account after five years? Pick the closest answer. a. $1,200.50 b. $1,220.20 c. $1,174.80 d. $1,217.50
b. $1,220.20 4% compounded quarterly → 4% ÷ 4 = 1% per quarter quarterly compounding over 5 years → 5×4 = 20 periods (quarters) PV -1,000 N 20 I/Y 1 → FV = $1,220.19
Claire 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: Pick the closest answer. a. $16,953 b. $15,002 c. $15,873 d. $16,417
b. $15,002 END mode PMT -5,043.71 N 4 I/Y 13 FV 0 → PV = $15,002.37
$2,000 invested today at 6% in 3 years would result in a future value of: Pick the closest answer. a. $2,000 b. $2,382 c. $6,362 d. $3,145
b. $2,382 PV -2,000 N 3 I/Y 6 → FV = $2,382.03
Lance would like to send his parents on a cruise for their 50th wedding anniversary. He expects the cruise will cost $15,000 and he has 5 years to accumulate this money. How much must Lance deposit at the end of each year in an account paying 10 percent interest in order to have enough money to send his parents on the cruise? Pick the closest answer. a. $1,136 b. $2,457 c. $1,193 d. $2,234
b. $2,457 END mode FV 15,000 PV 0 N 5 I/Y 10 → PMT = -$2,456.96
If we will receive $100 per year beginning one year from now for a period of three years with a 12% discount rate, what would be the value of our investment today? Pick the closest answer. a. $230 b. $240 c. $250 d. $260
b. $240 END mode PMT 100 FV 0 N 3 I/Y 12 → PV = $240.18
The future value of $200 received today and deposited at 8 percent for three years is: Pick the closest answer. a. $248.00 b. $251.94 c. $370.19 d. $218.55
b. $251.94 PV -200 N 3 I/Y 8 → FV = $251.94
An investment will mature in 20 years. Its maturity value is $1,000. If the discount rate is 7%, what is the present value of the investment? Pick the closest answer. a. $178 b. $258 c. $276 d. $362
b. $258 PV 1,000 N 20 I/Y 7 → PV = $258.42
The present value of an annuity of $5,000 to be received at the beginning of each of the 6 years at a discount rate of 4% would be: Pick the closest answer. a. $26,210 b. $27,259 c. $17,326 d. $18,365
b. $27,259 BGN mode PMT 5,000 N 6 I/Y 4 FV 0 → PV = -$27,259.11
A generous benefactor to the local university plans to make a one-time endowment which would provide the university 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? Pick the closest answer. a. $300,000 b. $3,000,000 c. $750,000 d. $1,428,571
b. $3,000,000 (ENDOWMENT) x 5= $150,000 Endowment=150,000/0.05=$3,000,000
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: Pick the closest answer. a. $2,500 b. $3,045 c. $6,516 d. $2,856
b. $3,045 use the opportunity cost of 7% as the discount rate 1ST DEPOSIT: FV 1,000 N 1 I/Y 7 → PV = $934.58 2ND DEPOSIT: FV 1,200 N 2 I/Y 7 → PV = $1,048.13 3RD DEPOSIT: FV 1,300 N 3 I/Y 7 → PV = $1,061.87 TOTAL $3,044.58
You have just won a lottery! You will receive $50,000 a year beginning one year from now for 20 years. If your required rate of return is 10% , what is the present value of your winning lottery ticket? Pick the closest answer. a. $418,250 b. $425,700 c. $444,640 d. $453,850
b. $425,700 END mode PMT 50,000 N 20 I/Y 10 FV 0 → PV = $425,678.19
The present value of an annuity of $5,000 to be received at the end of every six months for 6 years at a 4% annual rate would be (Pick the closest answer.): a. $26,210 b. $52,877 c. $53,934 d. $27,259
b. $52,877 END mode PMT 5,000 N 12 I/Y 2 FV 0 → PV = -$52,876.71
You need $8,000 four years from now for a down payment on your future house. How much money must you deposit today if your credit union pays 5% interest compounded annually? Pick the closest answer. a. $6,269.59 b. $6,581.62 c. $6,394.12 d. $6,189.83
b. $6,581.62 FV 8,000 N 4 I/Y 5 → PV = $6,581.62
Taylor deposits $2,000 per year at the end of the year for the next 20 years into an IRA account that pays 6%. How much will Taylor have on deposit at the end of 20 years? Pick the closest answer. a. $67,520 b. $73,572 c. $81,990 d. $75,686
b. $73,572 END mode PV 0 N 20 I/Y 6 PMT -2,000 → FV = $73, 571.18
The future value of an ordinary annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is: Pick the closest answer. a. $17,549 b. $75,401 c. $19,655 d. $77,664
b. $75,401 END mode PMT -1,000 N 40 I/Y 3 PV 0 → FV = $75,401.26
Kristen has just purchased a used Mercedes for $18,995. She plans to make a $2,500 down payment on the new car. What is the amount of her monthly payment on the remaining loan if she must pay 12% annual interest on a 24-month car loan? Pick the closest answer. a. $759.53 b. $776.48 c. $894.16 d. $899.87
b. $776.48 $18,995 - $2,500 = $16,495 is the amount she borrows monthly payments with 12% annual interest → 12% ÷ 12 = 1% per month ordinary annuity unless stated otherwise END mode PV 16,495 N 24 I/Y 1 FV 0 → PMT = $776.48
