Module 3 Test
Assume a bank loan requires an interest payment of $1,200 per year and a principal payment of $20,000 at the end of an eight-year life. a. At what amount could this loan be sold to another bank if loans of similar quality carried a 8.5% interest rate? That is, what would be the Present Value of this loan to the nearest dollar? b. Now, if interest rates on other similar quality loans are 10%, what would be the PV of his loan to the nearest dollar? c. What would be the PV of this loan if the interest rate is 6.5% on similar quality loans to the nearest dollar?
$ ___17,180______________ $ ___15,732______________ $ __19,392_______________
To pay for your child's education, you wish to have accumulated $20,000 at the end of 9 years. To do this, you plan on depositing an equal amount into the bank at the end of each year. If the bank is willing to pay 12 percent compounded annually, how much must you deposit each year to reach your goal?
$1353.58
You plan to accumulate $450,000 over a period of 12 years by making equal annual deposits in an account that pays an annual interest rate of 9% (assume all payments will occur at the beginning of each year). What amount must you deposit each year to reach your goal?
$20,497.98
Bob Terwilliger received $12,345 for his services as financial consultant to the mayor's office of his hometown of Springfield. Bob says that his consulting work was his civic duty and that he should not receive any compensation. So, he has invested his paycheck into an account paying 3.98 percent annual interest and left the account in his will to the city of Springfield on the condition that the city cannot collect any money from the account for 200 years. How much money will the city receive from Bob's generosity in 200 years?
$30300773.41
You plan on buying some property in Florida 5 years from today. To do this, you estimate that you will need $20,000 at that time for the purchase. You would like to accumulate these funds by making equal annual deposits in your savings account, which pays 12 percent annually. If you make your first deposit at the end of this year, and you would like your account to reach $20,000 when the final deposit is made, what will be the amount of your deposits? The amount of your end-of-year deposits will be
$3148.19
On December 31, Beth Klemkosky bought a yacht for $50,000, paying $10,000 down and agreeing to pay the balance in 10 equal end-of-year installments at 10 percent interest on the declining balance. How big will the annual payments be?
$6509.82
If you'd like to have $5,000,000 at retirement in 45 years and you expect to earn 10 percent annually, which is around the average return over the past 50 years, what lump sum would you have to invest today? The lump sum you would have to invest today is
$68,596.04
You have an uncle wants to see you be successful in life. He has no children of his own, so he'd like to do something for you, but at the same time instill a good work ethic. He has promised to match up to 50% of what you make by working for your first 5 years of working. You have just graduated and found a job paying $50,000. You were wanting to know the present value of your uncle's gift. You elected to measure the gift using a 9.25% discount rate. What is the value of your uncle's gift to the nearest dollar?
$96,614
Betty borrows $60,000 at 12 percent compounded annually. The loan is to be repaid in five equal annual end-of-year installments. How much must each loan payment be?
$__16,645_________________
Cindy wants $2.5 million for her retirement at age 65. Cindy is 25 years old today and plans to deposit equal amounts each year starting on her 26th birthday and ending on her 65th birthday. If her investments earn 6% per year, how much must each deposit be to the nearest dollar? Hint:BEG
$___16,259________________
Suppose your Professor currently has no savings, but wants to retire in 30 years as a millionaire. If he can earn 8.75%, compounded annually on his investments, how much should he set aside in equal installments today to reach his goal? [Beg]
$___7,067________________
If you wish to accumulate $197,000 in 5 years, how much must you deposit today in an account that pays a quoted annual interest rate of 13% with semi-annual compounding of interest?
104,947
At what annual interest rate must $115,000 be invested so that it will grow to be $530,000 in 14 years?
11.5%
How many years will it take for $197,000 to grow to be $554,000 if it is invested in an account with a quoted annual interest rate of 8% with monthly compounding of interest to the nearest year?
13 years
Kirk Van Houten, who has been married for 23 years, would like to buy his wife an expensive diamond ring with a platinum setting on their 30-year wedding anniversary. Assume that the cost of the ring will be $12,000 in 7 years. Kirk currently has $4,510 to invest. What annual rate of return must Kirk earn on his investment to accumulate enough money to pay for the ring?
15.00%
How many years will it take for $136,000 to grow to be $468,000 if it is invested in an account with an annual interest rate of 8 % to the nearest year?
16 years
You just invested $50,000 into an account that earns 7 percent compounded annually. At the end of each year you can withdraw $4,971. How many years can you continue to make the withdrawals?
18 years
You've just received an offer from a bank for a credit card with a quoted rate, or APR, of 18 percent compounded monthly. What's the EAR, or effective annual rate, on the credit card?
19.56%
You lend a friend $30,000, which your friend will repay in 5 equal annual end-of-year payments of $10,000, with the first payment to be received 1 year from now. What rate of return does your loan receive?
19.86%
If you deposit $15,000 per year for 9 years (each deposit is made at the beginning of each year) in an account that pays an annual interest rate of 8%, what will your account be worth at the end of 9 years?
202.298
You lend a friend $10,000, for which your friend will repay you $27,027 at the end of 5 years. What interest rate are you charging your friend?
22%
If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
25,490
You made it! Your 50 years old and have a million dollars. You decide to retire and live off $70,000 a year. You have gotten conservative now that you are retired and can only get 5% return on your money? You plan to take annual distributions. How long will your money last to the nearest decimal (ex 11.1)?
25.7
In September 1963, the first issue of the comic book X-MEN was issued. The original price for that issue was $0.12. By September 2015, 52 years later, the value of the near-mint copy of this comic book had risen to $55,100. What annual rate of interest would you have earned if you had bought the comic in 1963 and sold it in 2015?
28.49%
You are told that if you invest $11,000 per year for 23 years (all payments made at the end of each year) you will have accumulated $366,000 at the end of the period. What annual rate of return is the investment offering?
3.21
What is the present value of $359,000 that is to be received at the end of twenty three years, the discount rate is 11% and annually discounting occurs?
32,559_________________ PV= 359,000[1/(1+.11)^23]=
If you deposit $16,000 per year for 12 years (each deposit is made at the end of each year) in an account that pays an annual interest rate of 14%, what will your account be worth at the end of 12 years?
436,332
Jack asked Jill to marry him, and she has accepted under one condition: Jack must buy her a new $330,000 Rolls-Royce Phantom. Jack currently has $45,530 that he may invest. He has found a mutual fund with an expected annual return of 4.5% in which he will place the money. How long will it take Jack to win Jill's hand in marriage? Ignore taxes.
45.0 years
You are told that if you invest $11,100 per year for 19 years (all payments made at the beginning of each year) you will have accumulated $375,000 at the end of the period. What annual rate of return is the investment offering?
5.48%
What will $153,000 grow to be in 13 years if it is invested today in an account with a quoted annual interest rate of 10% with monthly compounding of interest?
558,386
You plan to borrow $389,000 now and repay it in 25 equal annual installments (payments will be made at the end of each year). If the annual interest rate is 14%, how much will your annual payments be?
56,599
What will $247,000 grow to be in 9 years if it is invested today in an account with an annual interest rate of 11% with quarterly compounding?
655,908
If you were offered $1,079.50 10 years from now in return for an investment of $500 currently, what annual rate of interest would you earn if you took the offer?
8%
You are wanting to retire as a millionaire by the time you are 50. You are starting with nothing, but believe you could get an average return of 9% over the next 25 years. How much would you need to save monthly to get a million dollars by age 50?
891.96
You decide you want your child to be a millionaire. You have a son today and you deposit $10,000 in an investment account that earns 7% per year. The money in the account will be distributed to your son whenever the total reaches $1,500,000. How old will your son be when he gets the money (rounded to the nearest year)? A. 74 years B. 60 years C. 82 years D. 49 years
A. 74 years
U.S. Savings Bonds are sold at a discount. The face value of the bond represents its value on its future maturity date. Therefore, A. the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures in 5 years. B. the current price of a $50 face value bond that matures in 10 years will be greater than the current price of a $50 face value bond that matures in 5 years. C. the current prices of all $50 face value bonds will be the same, regardless of their maturity dates because they will all be worth $50 in the future. D. the current price of a $50 face value bond will be higher if interest rates increase.
A. the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures in 5 years.
The present value of $1,000 to be received in 5 years is ________ if the discount rate is 12.78%. A. $548 B. $368 C. $494 D. $687
A. $548
You finally graduated with your Masters. You got a great job, but now you need to pay back some loans ☹. You have $34,000 in loans and the interest rate is 6.8%. What would be your balance after 3 years? A. $26,093 B. $25,185 C. $26,795 D. $27,123
A. $26,093
The Garrett's are planning ahead for their son's education. He's eight now and will start college in 10 years. How much will they have to set aside at the end of each year to have $65,000 in 10 years if the annual interest rate is 7%? A. $4,705 B. $4,500 C. $3,976 D. $4,625
A. $4,705
How much will a investment of $650 per month be worth in eight years at an annual interest rate of 8 percent? A. $87,015 B. $87,595 C. $86,498 D. $87,758
A. $87,015
Using the above information, suppose you told the Lottery Commission said they would pay you at the beginning of each year for the next twenty years. The lottery commission will use a discount rate of 6%. What would be the lump sum value today of the twenty year payout? A. $40,000,000 B. $24,316,233 C. $25,394,327 D. $23,568,789
B. $24,316,233
You plan to go to Asia to visit friends in three years. The trip is expected to cost a total of $10,000 at that time. Your parents have deposited $5,000 for you in a Certificate of Deposit paying 6% interest annually, maturing three years from now. Uncle Lee has agreed to pay for all remaining expenses. If you are going to put Uncle Lee's gift in an investment earning 10% over the next three years, how much must he deposit today, so you can visit your friends three years from today? A. $3,757 B. $3,039 C. $5,801 D. $3,345
B. $3,039
You finally graduated with your Masters. You got a great job, but now you need to pay back some loans ☹. You have $34,000 in loans and the interest rate is 6.8%. How much do you need to pay monthly if you want to pay off in ten years? A. $381.21 B. $391.27 C. $376.54 D. $388.69
B. $391.27
You are ready to retire. A glance at your 401(k) statement indicates that you have $750,000. If the funds remain in an account earning 9.0%, how much could you withdraw at the beginning of each year for the next 25 years? A. $55,620 B. $70,050 C. $35,830 D. $2,500
B. $70,050
You would like to retire in 30 years by investing in your 401(k) plan at work. You make $50,000. Your employer will match dollar for dollar up to 5%, so you elect to contribute 5% of your salary to your 401(k). You will make monthly contributions to your 401(k). After reviewing the 401(k) investment choices, you expect to get a 9.5% return. Assuming you get no increases in salary in 30 years, how much will you have in your 401(k) in 30 years? A. $952,211 B. $847,097 C. $926,543 D. $828,982
B. $847,097
What is the monthly rate of interest that will yield an annual effective interest rate of 12 percent? A. 1.499% B. 0.949% C. 0.953% D. 1.949%
B. 0.949%
A credit card company states an annual percentage rate of 15% compounded monthly. What is the effective annual rate? A. 15.00% B. 16.07% C. 16.54% D. 16.75%
B. 16.07%
If Cathy deposits $12,000 into a bank account that pays 6% interest compounded quarterly, what will the account balance be in seven years? A. 18,001 B. 18,207 C. 19,112 D. 19,344
B. 18,207
Which of the following conclusions would be true if you earn a higher rate of return on your investments? A. The greater the present value would be for any lump sum you would receive in the future. B. The lower the present value would be for any lump sum you would receive in the future. C. Your rate of return would not have any effect on the present value of any sum to be received in the future. D. The greater the present value would be for any annuity you would receive in the future.
B. The lower the present value would be for any lump sum you would receive in the future.
The present value of a single future sum A. increases as the number of discount periods increases. B. is generally larger than the future sum. C. depends upon the number of discount periods. D. increases as the discount rate increases.
C. depends upon the number of discount periods.
How much money must be put into a bank account yielding 6.42% (compounded annually) in order to have $1,671 at the end of 11 years (round to nearest $1)? A. $798 B. $886 C. $843 D. $921
C. $843
A real estate appraiser has advised you that the value of the homes in your neighborhood has been rising at a compound annual rate of about 5% in recent years. On the basis of this information, what is the value today of the house you bought 8 years ago for $129,500? A. $ 180,754 B. $ 181,122 C. $ 191,330 D. $ 181,308
C. $ 191,330
It is January 1st and Steve Hein has just established an IRA (Individual Retirement Account). Steve will deposit $2,000 a year at the end of year for the following 39 years (40 years total). How much money will Steve have in his account at the end of the 40th year? Assume that the account pays 12% interest compounded annually. A. $1,087,197 B. $1,219,661 C. $1,534,183 D. $1,368,020
C. $1,534,183
Ms. Knight has won a scholarship which pays her $5,000 per year for 3 years starting a year from today. She is curious to know how much should would have needed to save to equal her scholarship. She wants to know the present value of the scholarship using a discount rate of 7%. A. $15,000 B. $14,164 C. $13,122 D. $13,789
C. $13,122
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? A. $3,124 B. $3,310 C. $3,641 D. $4,812
C. $3,641
You finally graduated with your Masters. You got a great job, but now you need to pay back some loans ☹. You have $34,000 in loans and the interest rate is 6.8%. What would be your balance after 3 years? Suppose you could re-finance the balance after three years at 4.6% with a 5 year loan. What would your payments be? A. $457.23 B. $445.65 C. $487.64 D. $519.29
C. $487.64
Augustus McRae deposited $10,000 in a savings account that paid 9 % interest compounded quarterly. What is the effective rate of interest? A. 9.00% B. 9.42% C. 9.31% D. 9.25%
C. 9.31%
A bond matures in 20 years, at which time it pays the owner $1,000. It also pays $70 at the end of each of the next 20 years. If similar bonds are currently yielding 7%, what is the market value of the bond? A. over $1,000 B. under $1,000 C. exactly $1,000 D. cannot be determined from the information given
C. exactly $1,000
The future value of a dollar ________ as the interest rate increases and ________ the farther in the future is the funds are to be received. A. decreases; decreases. B. decreases; increases. C. increases; increases. D. increases; decreases
C. increases; increases.
Lee 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? A. $14,900 B. $50,000 C. $117,453 D. $17,460
D. $17,460
Congratulations! You are the proud winner of the multi-state $40 million Sour Ball Lottery. You can receive $2,000,000 at the end of each year for the next 20 years or choose the "cash option" and receive a lump sum. If the discount rate is 7%, what is the value today of the 20 year payout option? A. $26,945,332 B. $29,707,503 C. $32,977,401 D. $21,188,028
D. $21,188,028
How much would you be willing to pay (rounded to the nearest dollar) for a 20-year cash flow if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year? A. $84,500 B. $63,445 C. $56,734 D. $53,777
D. $53,777
What is the present value of $11,463 to be received 7 years from today? Assume a discount rate of 3.5% compounded annually and round to the nearest $1. A. $5,790 B. $6,508 C. $7,210 D. $9,010
D. $9,010
What nominal annual interest rate is implied if you borrow $12,500 and repay $21,364.24 in three years with monthly compounding? A. 12% B. 15% C. 17% D. 18%
D. 18%
How long does it take for $5,000 to grow into $6,400 at 10% compounded quarterly? A. 2 years. B. 3 years. C. 4 years. D. 30 months.
D. 30 months.
You finally graduated with your Masters. You got a great job, but now you need to pay back some loans ☹. You have $34,000 in loans and the interest rate is 6.8%. How long would if take you to pay it off if you paid $500 per month? A. 6.25 years B. 6.60 years C. 6.90 years D. 7.20 years
D. 7.20 years
An investment earning simple interest is preferred over an investment earning compound interest because the simplicity adds value.
FALSE
The present value of an annuity increases as the discount rate increases.
FALSE
What will $247,000 grow to be in 9 years if it is invested today in an account with an annual interest rate of 11%?
FV= 247,000(1+.11)^9= 631,835
An investment earning simple interest is preferred over an investment earning compound interest because the simplicity adds value.
False
The present value of $1,000 to be received in 5 years is ________ if the discount rate is 12.78%. A. $368 B. $494. C. $548 D. $687
PV= 1000[1/.(1+.1278)^5]= 548
If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
PV= 140,000[1/(1+.14)^13] = 25,490
If you wish to accumulate $197,000 in 5 years, how much must you deposit today in an account that pays a quoted annual interest rate of 13%?
PV= 197,000[1/(1+.13)^5)]= 106,924
What is the value today of a future amount of $468,000 in 12 years if it is invested in an account with an annual interest rate of 8%?
PV= 468,000 [1/(1+.08)^12]= 185,849
A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate of deposit that pays 10% compounded only once per year.
TRUE
A timeline identifies the timing and amount of a stream of cash flows, along with the interest rate it earns.
TRUE
As the interest rate increases, present value decreases
TRUE
Discounting is an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value
TRUE
If the future value of annuity A is greater than the future value of annuity B, then the present value of annuity A must also be greater than the present value of annuity B.
TRUE
When using a financial calculator, cash outflows generally have to be entered as negative numbers, because a financial calculator sees money "leaving your hands."
TRUE
A timeline identifies the timing and amount of a stream of cash flows, along with the interest rate it earns.
True
Compound interest is interest earned on interest in addition to interest earned on the principal.
True
The time value of money is the opportunity cost of passing up the earning potential of a dollar today.
True
Tim invested $1,000 in a mutual fund paying 8% per year. John invested $500 in the same fund. If both Tim and John keep their money invested for the same period of time, Tim will end up with twice as much money as John.
True
You wish to accumulate $10,000 by depositing $481.46 per month into a savings account that earns 4.75% compounded monthly. How many monthly deposits must you make?
__20 years___________
Although you have made no deposits or withdrawals from your emergency fund account, the account value has risen during the past 3 years from $15,000 to $17,613.62. a.) What has been the compound annual interest rate that has been credited to your account? b.) At that rate, how many more years will be needed until your account balance reaches $20,000?
__5.5______ % __2.4___ years
You borrow $25,000 to buy a car, and agree to make 48 monthly payments of $607.39 to repay the loan. What annual rate of interest, which is being compounded monthly, are you being charged?
__7.75_______ %
To the closest year, how long will it take $35,000 to double if it is deposited and earns 6.25% compounded annually to the nearest decimal point?
___11.4_________ years
Which amount is worth more at 8.50% compounded annually: $1,000 in hand today or $2,000 due in 8 years?
____2,000_____________________
Stanford Simmons, who recently sold his Porsche, placed $10,000 in a savings account paying annual compound interest of 6 percent. a. Calculate the amount of money that will have accrued if he leaves the money in the bank for 1, 5, and 15 years. b. If he moves his money into an account that pays 8 percent or one that pays 10 percent, rework part a using these new interest rates. c. What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you have completed in this problem?
a. 10600 13382.26 23965.58 b. 10800 14693.28 31721.69 11000 16105.10 41772.48 c.There is a __positive__ relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues and the future value of that sum
At what annual rate would the following have to be invested? a. $500 to grow to $1,947.99 in 12 years b. $300 to grow to $422.13 in 7 years c. $50 to grow to $280.22 in 20 years d. $200 to grow to $497.66 in 5 years
a. 12% b. 5% c. 9% d. 20%
What is the present value of the following annuities? a. $2,400 a year for 10 years discounted back to the present at 11 percent. b. $80 a year for 5 years discounted back to the present at 8 percent. c. $270 a year for 11 years discounted back to the present at 11 percent. d. $450 a year for 4 years discounted back to the present at 4 percent.
a. 14134.16 b. 319.42 c. 1675.76 d. 1633.45
How many years will the following take? a. $500 to grow to $1,039.50 if invested at 5 percent compounded annually b. $35 to grow to $53.87 if invested at 9 percent compounded annually c. $100 to grow to $298.60 if invested at 20 percent compounded annually d. $53 to grow to $78.76 if invested at 2 percent compounded annually
a. 15 years b. 5 years c. 6 years d. 20 years
You are offered $1,000 today, $10,000 in 12 years, or $25,000 in 25 years. Assuming that you can earn 11 percent on your money, which offer should you choose? a. What is the present value of $25,000 in 25 years discounted at 11 percent interest rate? b. What is the present value of $10,000 in 12 years discounted at 11 percent interest rate? c. Which offer should you choose? A. Choose $25,000 in 25 years because its present value is the highest. B. Choose $10,000 in 12 years because its present value is the highest. C. Choose $1,000 today because its present value is the highest.
a. 1840.20 b. 2858.41 c. B. Choose $10,000 in 12 years because its present value is the highest.
Bart Simpson, age 10, wants to be able to buy a really cool new car when he turns 16.His really cool car costs $19,000 today, and its cost is expected to increase 4 percent annually. Bart wants to make one deposit today (he can sell his mint-condition original Nuclear Boy comic book) into an account paying 7.9 percent annually in order to buy his car in 6 years. How much will Bart's car cost, and how much does Bart have to save today in order to buy this car at age 16? a. How much will Bart's car cost after 6 years? b. How much does Bart have to save today in order to buy this car at age 16?
a. 24041.06 b. 15234.39
Imagine that Homer Simpson actually invested $100,000 5 years ago at a 7.5percent annual interest rate. If he invests an additional $1,500 a year at the beginning of each year for 20 years at the same 7.5 percent annual rate, how much money will Homer have 20 years from now? a. If Homer invested $100,000 5 years ago at a 7.5 percent annual interest rate, what is the future value of this investment 20 years from now? b. If Homer invests an additional $1,500 a year at the beginning of each year for 20 years at the same 7.5 percent annual rate, what is the future value of this investment 20 years from now? c. How much money will Homer have 20 years from now?
a. 609833.96 b. 69828.80 c. 679662.76
Nicki Johnson, a sophomore mechanical engineering student, receives a call from an insurance agent, who believes that Nicki is an older woman ready to retire from teaching. He talks to her about several annuities that she could buy that would guarantee her an annual fixed income. The annuities are as follows in the popup window: LOADING.... If Nicki could earn 9 percent on her money by placing it in a savings account, should she place it instead in any of the annuities? Which ones, if any? Why? A 50,000 6,000 16 B 60,000 9,000 12 C 80,000 8,500 25
a. 8.96% No. Nicki should not place her money in annuity A because the expected rate of return on the annuity is smaller than the one on the savings account b. 10.45% Yes. Nicki should place her money in annuity B because the expected rate of return on the annuity is greater than the one on the savings account. c. 9.53% Yes. Nicki should place her money in annuity C because the expected rate of return on the annuity is greater than the one on the savings account
In 13 years, you are planning on retiring and buying a house in Oviedo, Florida. The house you are looking at currently costs $130,000 and is expected to increase in value each year at a rate of 4 percent. Assuming you can earn 14 percent annually on your investments, how much must you invest at the end of each of the next 13 years to be able to buy your dream home when you retire? a. If the house you are looking at currently costs $130,000 and is expected to increase in value each year at a rate of 4 percent, what will the value of the house be when you retire in 13 years? b. Assuming you can earn 14 percent annually on your investments, how much must you invest at the end of each of the next 13 years to be able to buy your dream home when you retire?
a. value of house: 216459.56 b. invest: 6745.66
The present value of a single future sum increases as the number of discount periods increases. is generally larger than the future sum. depends upon the number of discount periods. decreases as the discount rate increases.
decreases as the discount rate increases.
Assuming two investments have equal lives, a high discount rate tends to favor the investment with large cash flow early. the investment with large cash flow late. the investment with even cash flow. neither investment since they have equal lives.
the investment with large cash flow early.
