Final Prep III
In 1884, the winner of a competition was paid $100. In 2015, the winner's prize was $375,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate? (Round your answer to the nearest $500.)
$,1,803,500 $375,000 = $100 ×(1 + r)131; r = 6.48359 percent FV = $375,000 ×(1 + .0648359)25 = $1,803,500 (rounded to nearest $500)
You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 6 percent, compounded monthly. What will be your monthly payment?
$1,058.01 PVA Due = $55,000 = C × [(1 - {1 / [1 + (.06 / 12)]60}) / (.06 / 12)] × [1 + (.06 / 12)] C = $1,058.01
Phil can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, how much can he afford to borrow to purchase a car?
$11,697.88 PVA = $240 × [(1 - {1 / [1 + (.085 / 12)](5 × 12)}) / (.085 / 12)] = $11,697.88
Alex invested $10,500 in an account that pays 6 percent simple interest. How much money will he have at the end of four years?
$13,020 Ending value = $10,500 + ($10,500 ×.06 ×4) = $13,020
Imprudential, Inc. has an unfunded pension liability of $627 million that must be paid in 21 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. The relevant discount rate is 7.38 percent. What is the present value of this liability?
$140,564,661 PV = $627,000,000/(1.0738)21 = $140,564,661
You collect old coins. Today, you have two coins each of which is valued at $100. One coin is expected to increase in value by 5.2 percent annually while the other coin is expected to increase in value by 5 percent annually. What will be the difference in the value of the two coins 25 years from now?
$16.50 Future value = $100 ×(1 + .052)25 = $355.14 Future value = $100 ×(1 + .05)25 = $338.64 Difference = $355.14 - 338.64 = $16.50
Jones Stoneware has a $65,000 liability it must pay four years from today. The company is opening a savings account so that the entire amount will be available when this debt comes due. The plan is to make an initial deposit today and then deposit an additional $10,000 at the end of each of the four years. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today?
$18,631.23 FVA = $10,000 × {[(1 + .045)4 - 1] / .045} = $42,781.91 Additional FV needed = $65,000 - 42,781.91 = $22,218.09 Initial deposit = $22,218.09 / 1.0454 = $18,631.23
A newly issued 20-year, $1,000, zero coupon bond just sold for $311.05. What is the implicit interest, in dollars, for the first year of the bond's life? Assume semiannual compounding.
$18.70 Bond price 0 = $311.05 = $1,000 / [1 + (r / 2)](20 × 2); r = 5.925% Bond price 1 = $1,000 / [1 + (.05925 / 2)](19 × 2) = $329.75 Implicit interest = $329.75 - 311.05 = $18.70
You would like to establish a trust fund to provide $140,000 a year forever for your heirs. The expected rate of return is 5.45 percent. How much money must you deposit today to fund this gift?
$2,568,807 PV = $140,000 / .0545 = $2,568,807
You purchased an investment that will pay you $8,000, in real dollars, a year for the next three years. Each payment will be received at the end of the period with the first payment occurring one year from today. The nominal discount rate is 9.897 percent and the inflation rate is 2.9 percent. What is the present value of these payments in real dollars?
$21,072 You need to discount real dollars with the real interest rate. r = 1.09897 / 1.029 - 1 = .0680, or 6.80% PV = $8,000 × ({1 - [1 / (1 + .068)3]} / .068) = $21,072
Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?
$261,172
Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,400 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75 percent?
$27,677.34
Your employer contributes $60 a week to your retirement plan. Assume you work for your employer for another 20 years and the applicable discount rate is 9 percent. Given these assumptions, what is this employee benefit worth to you today?
$28,927.38 PVA = $60 × [(1 - {1 / [1 + (.09 / 52)](20 × 52)}) / (.09 / 52)] = $28,927.38
Travis invested $8,250 in an account that pays 4 percent simple interest. How much more could he have earned over a 7-year period if the interest had compounded annually?
$296.44 Simple interest = $8,250 + ($8,250 × .04 × 7) = $10,560 Compound interest = $8,250 × (1 + .04)7 = $10,856.44 Difference = $10,856.44 - 10,560 = $296.44
You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20-year withdrawal period?
$3,113.04 FVA = $1,100 ×({[1 + (.07 / 12)](15 ×12) - 1} / (.07 / 12)) + $500 ×({[1 + (.04 / 12)] (15 × 12) - 1} / (.04 / 12)) = $471,703.77 PVA = $471,703.77 = C ×[(1 - {1 / [1 + (.05 / 12)](20 × 12)}) / (.05 / 12)] C = $3,113.04
What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?
$38,125.20 Future value = $11,600 ×(1 + .0725)17 = $38,125.20
You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $21,500 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?
$398,148 GPPV = $21,500 / (.079 - .025) = $398,148
You just received $25,000 from an insurance settlement and have decided to invest it for your retirement. Currently, your goal is to retire 40 years from today. How much more will you have in your account on the day you retire if you can earn an average return of 8.2 percent rather than just 8 percent?
$41,718.03 Future value = $25,000 ×(1 + .082)40 = $584,831.07 Future value = $25,000 ×(1 + .08)40 = $543,113.04 Difference = $584,831.07 - 543,113.04 = $41,718.03
You want to be a millionaire when you retire in 40 years and can earn an annual return of 12.5 percent. How much more will you have to save each month if you wait 15 years to start saving versus if you start saving at the end of this month?
$414.34 FVA 40 years = $1,000,000 = C × ({[1 + (.125 / 12)](40 × 12) - 1} / (.125 / 12)) C = $72.53 FVA 25 years = $1,000,000 = C × ({[1 + (.125 / 12)](25 × 12) - 1} / (.125 / 12)) C = $486.87 Difference = $486.87 - 72.53 = $414.34
Racing Engines wants to save $750,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal?
$42,337.00 FVA Due = $750,000 = C × ({[1 + (.0475 / 4)](4 × 4) - 1} / (.0475 / 4)) × [1 + (.0475 / 4)] C = $42,337.00
This morning, you borrowed $162,000 to buy a house. The mortgage rate is 4.35 percent. The loan is to be repaid in equal monthly payments over 20 years with the first payment due one month from today. Assume each month is equal to 1/12 of a year and all taxes and insurance premiums are paid separately. How much of the second payment applies to the principal balance?
$426.11 162,000 = C ×[(1 - {1 / [1 + (.0435 / 12)](20 ×12)}) / (.0435 / 12)] C = $1,011.82 Interest Month 1 = $162,000 × (.0435 / 12) = $587.25 Principal Month 1 = $1,011.82 - 587.25 = $424.57 Principal balance Month 1 = $162,000 - 424.57 = $161,575.43 Interest Month 2 = $161,575.43 × (.0435 / 12) = $585.71 Principal Month 2 = $1,011.82 - 585.71 = $426.11
You want to start your own consulting business and believe it could produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $450,000. At a 14 percent discount rate, what is this business idea worth today?
$430,109 PV = $5,600 / 1.14 + $48,200 / 1.142 + ($125,000 + 450,000) / 1.143 = $430,109
Your older sister deposited $2,000 today at 6.5 percent interest for 5 years. You would like to have just as much money at the end of the next 5 years as your sister will have. However, you can only earn 6 percent interest. How much more money must you deposit today than your sister did if you are to have the same amount at the end of the 5 years?
$47.62 Future value = $2,000 ×(1 + .065)5 = $2,740.17 Present value = $2,740.17/(1 + .06)5 = $2,047.62 Difference = $2,047.62 - 2,000 = $47.62
You have just received notification that you have won the $1.25 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, 76 years from now. The appropriate discount rate is 6.8 percent. What is the present value of your winnings?
$8,423.54 PV = $1,250,000/(1.068)76 = $8,423.54
Al invested $7,200 in an account that pays 4 percent simple interest. How much money will he have at the end of five years?
$8,640 Ending value = $7,200 + ($7,200 ×.04 ×5) = $8,640
Theo needs $40,000 as a down payment for a house 6 years from now. He earns 2.5 percent on his savings. Theo can either deposit one lump sum today for this purpose or he can wait a year and deposit a lump sum. How much additional money must he deposit if he waits for one year rather than making the deposit today?
$862.30 Present value = $40,000/(1 + .025)6 = $34,491.87 Present value = $40,000/(1 + .025)5 = $35,354.17 Difference = $35,354.17 - 34,491.87 = $862.30
A year ago, you deposited $30,000 into a retirement savings account at a fixed rate of 5.5 percent. Today, you could earn a fixed rate of 6.5 percent on a similar type account. However, your rate is fixed and cannot be adjusted. How much less could you have deposited last year if you could have earned a fixed rate of 6.5 percent and still have the same amount as you currently will when you retire 38 years from today?
$9,234.97 less Future value = $30,000 ×(1 + .055)39 = $242,084.61 Present value = $242,084.61/(1 + .065)39 = $20,765.03 Difference = $30,000 - 20,765.03 = $9,234.97
You own a classic car that is currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?
$92,691.08 Future value = $64,000 ×(1 + .025)15 = $92,691.08
Oil Wells offers 6.5 percent coupon bonds with semiannual payments and a yield to maturity of 6.94 percent. The bonds mature in seven years. What is the market price per bond if the face value is $1,000?
$975.93 Bond price = $32.50 × [(1 − {1 / [1 + (.0694 / 2)](7 × 2)}) / (.0694 / 2)] + $1,000 / [1 + (.0694 / 2)](7 × 2) Bond price = $975.93
A 10-year, 4.5 percent, semiannual coupon bond issued by Tyler Rentals has a $1,000 face value. The bond is currently quoted at 98.7. What is the clean price of this bond if the next interest payment will occur 2 months from today?
$987.00 Clean price = .987 × $1,000 = $987
A 13-year, 6 percent coupon bond pays interest semiannually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent?
1.79 percent decrease Bond price = $30 × [(1 − {1 / [1 + (.055 / 2)](13 × 2)}) / (.055 / 2)] + $1,000 / [1 + (.055 / 2)](13 × 2) Bond price = $1,046.01 Bond price = $30 × [(1 - {1 / [1 + (.057 / 2)](13 × 2)}) / (.057 / 2)] + $1,000/ [1 + (.057 / 2)](13 × 2) Bond price = $1,027.28 Percentage change in price = ($1,027.28 - 1,046.01) / $1,046.01 = −.0179, or −1.79%
You are considering a one-year discount loan of $16,000. The interest rate is quoted as 7 percent plus 4 points. What is the actual rate you are paying on this loan?
11.46 percent Loan amount received = $16,000 ×(1 − 04) = $15,360 Loan repayment amount = $16,000 ×1.071 = $17,120 $17,120 = $15,360 ×(1 + r)1 r = 11.46 percent
Kaiser Industries has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and selling for $1,382.01. At this price, the bonds yield 7.5 percent. What is the coupon rate?
12.00 percent Bond price = $1,382. 01 = C × ({1 - [1 / (1 + .075)14]} / .075) + $1,000 / (1 + .075)14 C = $120 Coupon rate = $120 / $1,000 = .12, or 12%
Global Exporters wants to raise $29.6 million to expand its business. To accomplish this, it plans to sell 20-year, $1,000 face value, zero coupon bonds. The bonds will be priced to yield 7.75 percent. What is the minimum number of bonds it must sell to raise the money it needs? Assume semiannual compounding.
135,436 Bond price = $1,000 / [1 + (.0775 / 2)](20 × 2) = $218.554 Number of bonds = $29,600,000 / $218.544 = 135,436 bonds
The zero coupon bonds of JK Industries have a market price of $211.16, a face value of $1,000, and a yield to maturity of 7.39 percent. How many years is it until these bonds mature? Assume semiannual compounding.
21.43 years Bond price = $211.16 = $1,000 / [1 + (.0739 / 2)](t × 2) t = 21.43 years
Your local pawn shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans?
25.80 percent EAR = [1 + (.23 / 52)]52 - 1 = .2580, or 25.80 percent
MBM estimates its expansion cost at $18.63 million and wants it fully funded upfront. Management has decided to save $1.1 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on its savings. How long does the firm have to wait before expanding its operations?
3.79 years FVA = $18.63m = $1.1m × ({[1 + (.0625 / 4)]t - 1} / (.0625 / 4)) t = 15.143 quarters, or 3.79 years
You expect to receive $5,000 at graduation in 2 years. You plan on investing this money at 9 percent until you have $75,000. How many years from today will it be until this occurs?
33.42 years $75,000 = $5,000 ×(1.09)t; t = 31.42 years Total time = 2 + 31.42 = 33.42 years
You just paid $750,000 for an annuity that will pay you and your heirs $36,000 a year forever. What rate of return are you earning on this policy?
4.80 percent r = $36,000 / $750,000 = .048, or 4.80 percent
A corporate bond is quoted at a price of 98.96 and has a coupon rate of 4.8 percent, paid semiannually. What is the current yield?
4.85 percent
Al is retired and his sole source of income is his bond portfolio. Although he has sufficient principal to live on, he only wants to spend the interest income and thus is concerned about the purchasing power of that income. Which one of the following bonds should best ease Al's concerns?
5-year TIPS
Your father helped you start saving $20 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?
5.15 percent FVA Due = $6,528.91 = $20 × ({[1 + (r / 12)](17 × 12) - 1} / (r / 12)) × [1 + (r / 12)] r = 5.15 percent
Assume the average vehicle selling price in the United States last year was $35,996. The average price 4 years earlier was $29,208. What was the annual increase in the selling price over this time period?
5.36 percent $35,996 = $29,208 ×(1 + r)4; r = 5.36 percent
A $1,000 face value bond has a coupon rate of 7 percent, a market price of $911.02, and 10 years left to maturity. Interest is paid semiannually. If the inflation rate is 2.8 percent, what is the yield-to-maturity when expressed in real terms?
5.38 percent $911.02 = $35 × ({1 - [1 / (1 + r)(10 ×2)]} / r) + $1,000 / (1 + r)(10 ×2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 20 -911.02 35 1,000 N I/Y PV PMT FV Solve for: 4.1643 YTM = 2 × 4.1643% = 8.33% r = 1.0833 / 1.028 - 1 = 5.38%
You're trying to save to buy a new $72,000 sports car You have $38,000 today that can be invested at your bank. The bank pays 1.26 percent annual interest on its accounts. How many years will it be before you have enough to buy the car assuming the price of the car remains constant?
51.04 years $72,000 = $38,000 ×(1 + .0126)t; t = 51.04 years
The 7 percent bonds issued by Modern Kitchens pay interest semiannually, mature in eight years, and have a $1,000 face value. Currently, the bonds sell for $1,032. What is the yield to maturity?
6.48 percent $1,032 = $35 × [(1 − {1 / [1 + (r / 2)](8 × 2)}) / (r / 2)] + $1,000 / [1 + (r / 2)](8 × 2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 16 −1,032 35 1,000 N I/Y PV PMT FV Solve for: 3.2405 YTM = 2 × 3.2405% = 6.48%
One year ago, you invested $1,800. Today it is worth $1,924.62. What rate of interest did you earn?
6.92 percent $1,924.62 = $1,800 ×(1 + r)1; r = 6.92 percent
Sunset Sales has 7.2 percent coupon bonds on the market with 11 years left to maturity. The bonds make semiannual payments and currently sell for 98.6 percent of par. What is the effective annual yield?
7.52 percent $986 = $36 × ({1 - [1 / (1 + r)(11 × 2)]} / r) + $1,000 / (1 + r)(11 × 2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 22 -986 36 1,000 N I/Y PV PMT FV Solve for: 3.694 YTM = 2 × 3.694% = 7.388% Effective annual rate = [1 + (.07388 / 2)]2 - 1 = 7.52 percent
What is the effective annual rate if a bank charges you an APR of 8.25 percent, compounded quarterly?
8.51 percent EAR = [1 + (.0825 / 4)]4 - 1 = .0851, or 8.51 percent
Ten years ago, Jackson Supply set aside $130,000 in case of a financial emergency. Today, that account has increased in value to $330,592. What rate of interest is the firm earning on this money?
9.78 percent $330,592 = $130,000 ×(1 + r)10; r = 9.78 percent
The interest rate that is most commonly quoted by a lender is referred to as which one of the following?
Annual percentage rate.
Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at year 5 and an annual percentage rate of 10 percent?
Annual.
You are comparing two annuities that offer quarterly payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?
Annuity B has a smaller present value than annuity A.
The banks in your area offer the following rates of interest on their savings accounts. If you want to open one of these accounts, which bank should you select? Bank A: .75 percent APR with daily compounding. Bank B: .85 percent APR with monthly compounding. Bank C: .8725 percent APR with annual compounding. Bank D: .87 percent APR with quarterly compounding. Bank E: .775 percent APR with semi-annual compounding.
Bank D Bank A: EAR = [1 + (.0075 / 365)]365 - 1 = .007528, or .7528 percent Bank B: EAR = [1 + (.0085 / 12)]12 - 1 = .008533, or .8533 percent Bank C: EAR = (1 +.008725)1 - 1 = .008725, or .8725 percent Bank D: EAR = [1 + (.0087 / 4)]4 - 1 = .008728, or .8728 percent Bank E: EAR = [1 + (.0775 / 2)]2 - 1 = .007765, or .7765 percent
A bond that is payable to whomever has physical possession of the bond is said to be in:
Bearer form.
A $1,000 face value bond can be redeemed early at the issuer's discretion for $1,030, plus any accrued interest. The additional $30 is called the:
Call premium.
You are trying to compare the present values of two separate streams of cash flows that have equivalent risks. One stream is expressed in nominal values and the other stream is expressed in real values. You decide to discount the nominal cash flows using a nominal annual rate of 8 percent. What rate should you use to discount the real cash flows?
Comparable real rate.
Interest earned on both the initial principal and the interest reinvested from prior periods is called:
Compound interest.
Christina invested $3,000 five years ago and earns 2 percent interest on her investment. By leaving her interest earnings in her account, she increases the amount of interest she earns each year. The way she is handling her interest income is referred to as which one of the following?
Compounding.
Allison just received her semiannual payment of $35 on a bond she owns. Which term refers to this payment?
Coupon.
Jason's Paints just issued 20-year, 7.25 percent, unsecured bonds at par. These bonds fit the definition of which one of the following terms?
Debenture.
Which of these will increase the present value of an amount to be received sometime in the future?
Decrease in the interest rate.
Rosita paid a total of $1,189 to purchase a bond that has 7 of its initial 20 years left until maturity. This price is referred to as the:
Dirty price.
Today, June 15, you want to buy a bond with a quoted price of 98.64. The bond pays interest on January 1 and July 1. Which one of the following prices represents your total cost of purchasing this bond today?
Dirty price.
Steve just computed the present value of a $10,000 bonus he will receive in the future. The interest rate he used in this process is referred to as which one of the following?
Discount rate.
The process of determining the present value of future cash flows in order to know their worth today is referred to as:
Discounted cash flow valuation.
According to the Rule of 72, you can do which one of the following?
Double your money in 5 years at 14.4 percent interest.
A sinking fund is managed by a trustee for which one of the following purposes?
Early bond redemption.
An interest rate on a loan that is compounded monthly but expressed as an annual rate would be an example of which one of the following rates?
Effective annual rate.
You are investing $100 today in a savings account at your local bank. Which one of the following terms refers to the value of this investment one year from now?
Future value.
Treasury bonds are:
Generally issued as semi-annual coupon bonds.
You want to have $1 million in your savings account when you retire. You plan on investing a single lump sum today to fund this goal. You will earn 7.5 percent annual interest. Which of the following will reduce the amount that you must deposit today if you are to have your desired $1 million on the day you retire? I. Invest in a different account paying a higher rate of interest. II. Invest in a different account paying a lower rate of interest. III. Retire later. IV. Retire sooner.
I and III only.
Your grandmother has promised to give you $10,000 when you graduate from college. She is expecting you to graduate three years from now. What happens to the present value of this gift if you speed up your graduation by one year and graduate two years from now?
Increases.
Real rates are defined as nominal rates that have been adjusted for which of the following?
Inflation.
A "fallen angel" is a bond that has moved from:
Investment grade to speculative grade.
Which one of the following variables is the exponent in the present value formula?
Number of time periods
Four years ago, Seegee invested $500. Three years ago, Trek invested $600. Today, these two investments are each worth $800. Assume each account continues to earn its respective rate of return. Which one of the following statements is correct concerning these investments?
One year ago, Seegee's investment was worth less than Trek's investmen
The entire repayment of which one of the following loans is computed simply by computing one single future value?
Pure discount loan.
Sue is considering purchasing a bond that will only return its principal at maturity if the stock market declines. However, if the stock market increases in value during the bond term, at maturity, she will receive both the bond principal and a percentage of the stock market gain. What type of bond is th
Structured note.
This afternoon, you deposited $1,000 into a retirement savings account. The account will compound interest at 6 percent annually. You will not withdraw any principal or interest until you retire in 40 years. Which one of the following statements is correct?
The present value of this investment is equal to $1,000.
