65.
|
Your grandfather left you an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $3,000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Growing annuity |
66.
|
You just won a national sweepstakes! For your prize, you opted to receive never-ending payments. The first payment will be $12,500 and will be paid one year from today. Every year thereafter, the payments will increase by 3.5 percent annually. What is the present value of your prize at a discount rate of 8 percent?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Growing perpetuity |
67.
|
A wealthy benefactor just donated some money to the local college. This gift was established to provide scholarships for worthy students. The first scholarships will be granted one year from now for a total of $35,000. Annually thereafter, the scholarship amount will be increased by 5.5 percent to help offset the effects of inflation. The scholarship fund will last indefinitely. What is the value of this gift today at a discount rate of 9 percent?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Growing perpetuity |
68.
|
Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. Southern Tours has determined that a 13.5 percent rate of return is applicable to this potential acquisition. What is Southern Tours willing to pay today to acquire Holiday Vacations?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
69.
|
You are considering two savings options. Both options offer a 7.4 percent rate of return. The first option is to save $900, $1,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
70.
|
Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
71.
|
You are considering changing jobs. Your goal is to work for three years and then return to school full-time in pursuit of an advanced degree. A potential employer just offered you an annual salary of $41,000, $43,000, and $46,000 a year for the next three years, respectively. All salary payments are made as lump sum payments at the end of each year. The offer also includes a starting bonus of $3,000 payable immediately. What is this offer worth to you today at a discount rate of 6.75 percent?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
72.
|
You are considering a project which will provide annual cash inflows of $4,500, $5,700, and $8,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a 9 percent discount rate?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
73.
|
You just signed a consulting contract that will pay you $38,000, $52,000, and $85,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a 10.5 percent discount rate?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
74.
|
You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
75.
|
Your local travel agent is advertising an upscale winter vacation package for travel three years from now to Antarctica. The package requires that you pay $20,000 today, $35,000 one year from today, and a final payment of $45,000 on the day you depart three years from today. What is the cost of this vacation in today's dollars if the discount rate is 9.75 percent?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
76.
|
One year ago, Deltona Motor Parts deposited $16,500 in an investment account for the purpose of buying new equipment three years from today. Today, it is adding another $12,000 to this account. The company plans on making a final deposit of $20,000 to the account one year from today. How much will be available when it is ready to buy the equipment, assuming the account pays 5.5 interest?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
77.
|
Lucas will receive $7,100, $8,700, and $12,500 each year starting at the end of year one. What is the future value of these cash flows at the end of year five if the interest rate is 9 percent?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
78.
|
You plan on saving $5,200 this year, nothing next year, and $7,500 the following year. You will deposit these amounts into your investment account at the end of each year. What will your investment account be worth at the end of year three if you can earn 8.5 percent on your funds?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
79.
|
Miley expects to receive the following payments: Year 1 = $50,000; Year 2 = $28,000; Year 3 = $12,000. All of this money will be saved for her retirement. If she can earn an average of 10.5 percent on her investments, how much will she have in her account 25 years after making her first deposit?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
80.
|
Blackwell, Inc. has a $75,000 liability it must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $15,000 each year for the next three years, starting one year from today. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
81.
|
The government has imposed a fine on the Corner Tavern. The fine calls for annual payments of $125,000, $100,000, $75,000, and $50,000, respectively, over the next four years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including the investment earnings, to help the local community shelter. The government will earn 5.5 percent on the funds held. How much will the community shelter receive four years from today?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
82.
|
Wicker Imports established a trust fund that provides $90,000 in scholarships each year for needy students. The trust fund earns a fixed 6 percent rate of return. How much money did the firm contribute to the fund assuming that only the interest income is distributed?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.2 Topic: Perpetuity present value |
83.
|
A preferred stock pays an annual dividend of $3.20. What is one share of this stock worth today if the rate of return is 11.75 percent?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.2 Topic: Perpetuity present value |
84.
|
You would like to establish a trust fund that will provide $120,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 5.75 percent. How much money must you deposit today to fund this gift for your heirs?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.2 Topic: Perpetuity present value |
85.
|
You just paid $750,000 for an annuity that will pay you and your heirs $42,000 a year forever. What rate of return are you earning on this policy?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Perpetuity |
86.
|
You grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the rate of return?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Perpetuity rate |
87.
|
The preferred stock of Casco has a 6.25 percent dividend yield. The stock is currently priced at $59.30 per share. What is the amount of the annual dividend?
C = $59.30 × 0.0625 = $3.71
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Annuity payment |
88.
|
Your credit card company charges you 1.65 percent interest per month. What is the annual percentage rate on your account?
APR = 0.0165 × 12 = 19.80 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Annual percentage rate |
89.
|
What is the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter?
APR = 0.0275 × 4 = 11.00 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Annual percentage rate |
90.
|
You are paying an effective annual rate of 18.974 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Annual percentage rate |
91.
|
What is the effective annual rate if a bank charges you 8.25 percent compounded quarterly?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective annual rate |
92.
|
Your credit card company quotes you a rate of 17.9 percent. Interest is billed monthly. What is the actual rate of interest you are paying?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective interest rate |
93.
|
The 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?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective annual rate |
94.
|
You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective annual rate |
95.
|
You have $5,600 that you want to use to open a savings account. There are five banks located in your area. The rates paid by banks A through E, respectively, are given below. Which bank should you select if your goal is to maximize your interest income?
EARA = 4.61 percent
Bank C offers the highest effective annual rate at 4.622 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective annual rate |
96.
|
What is the effective annual rate of 14.9 percent compounded continuously?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Continuous compounding |
97.
|
What is the effective annual rate of 5.25 percent compounded continuously?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Continuous compounding |
98.
|
City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.75 percent annual percentage rate on its loans. What is the maximum rate the bank can actually earn based on the quoted rate?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Continuous compounding |
99.
|
You are going to loan a friend $550 for one year at a 6 percent rate of interest, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually?
Additional interest = $550 × (0.0618365 - 0.06) = $1.01 |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Interest compounding |
100.
|
You are borrowing money today at 8.48 percent, compounded annually. You will repay the principal plus all the interest in one lump sum of $12,800 two years from today. How much are you borrowing?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.4 Topic: Pure discount loan |
101.
|
This morning, you borrowed $9,500 at 8.9 percent annual interest. You are to repay the loan principal plus all of the loan interest in one lump sum four years from today. How much will you have to repay?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Pure discount loan |
102.
|
On this date last year, you borrowed $3,400. You have to repay the loan principal plus all of the interest six years from today. The payment that is required at that time is $6,000. What is the interest rate on this loan?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Pure discount loan |
103.
|
John's Auto Repair just took out a $52,000, 10-year, 8 percent, interest-only loan from the bank. Payments are made annually. What is the amount of the loan payment in year 10?
Payment in year 10 = $52,000 + ($52,000 × 0.08) = $56,160
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Interest-only loan |
104.
|
On the day you entered college, you borrowed $18,000 on an interest-only, four-year loan at 5.25 percent from your local bank. Payments are to be paid annually. What is the amount of your loan payment in year 2?
Payment in year 2 = $18,000 × 0.0525 = $945
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Interest-only loan |
105.
|
On the day you entered college you borrowed $30,000 from your local bank. The terms of the loan include an interest rate of 4.75 percent. The terms stipulate that the principal is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much total interest will you pay on this loan?
Total interest paid = $30,000 × 0.0475 × 5 = $7,125.00
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Interest-only loan |
106.
|
You just acquired a mortgage in the amount of $249,500 at 6.75 percent interest, compounded monthly. Equal payments are to be made at the end of each month for thirty years. How much of the first loan payment is interest? (Assume each month is equal to 1/12 of a year.)
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.4 Topic: Amortized loan |
107.
|
On June 1, you borrowed $220,000 to buy a house. The mortgage rate is 8.25 percent. The loan is to be repaid in equal monthly payments over 15 years. The first payment is due on July 1. How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.2 Topic: Amortized loan |
108.
|
This morning, you borrowed $150,000 to buy a house. The mortgage rate is 7.35 percent. The loan is to be repaid in equal monthly payments over 20 years. The first payment is due one month from today. How much of the second payment applies to the principal balance? (Assume that each month is equal to 1/12 of a year.)
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 06-03 How loans are amortized or paid off. Section: 6.2 Topic: Amortized loan |
109.
|
Western Bank offers you a $21,000, 9-year term loan at 8 percent annual interest. What is the amount of your annual loan payment?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 6-9 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Loan payment |
110.
|
First Century Bank wants to earn an effective annual return on its consumer loans of 10 percent per year. The bank uses daily compounding on its loans. By law, what interest rate is the bank required to report to potential borrowers?
APR = 365 × [(1 + 0.10)1/365 - 1] = 9.53 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-15 Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Interest rate |
111.
|
Downtown Bank is offering 2.2 percent compounded daily on its savings accounts. You deposit $8,000 today. How much will you have in your account 11 years from now?
FV = $8,000 × [1 + (0.022/365)]11 × 365 = $10,190.28
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 6-17 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Future value |
112.
|
You want to buy a new sports coupe for $41,750, and the finance office at the dealership has quoted you an 8.6 percent APR loan compounded monthly for 48 months to buy the car. What is the effective interest rate on this loan?
EAR = [1 + (.086/12)]12 - 1 = 8.95 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 6-20 Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective interest rate |
113.
|
Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses over the next 4 years. The account pays 1.25 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next 4 years?
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 6-26 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present value |
114.
|
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?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 6-32 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Annuity payment |
115.
|
You want to be a millionaire when you retire in 40 years. You can earn A 12.5 percent annual return. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month?
FVA40 years = $1,000,000 = C × [{[1 + (0.125/12)]40 × 12; C = $72.53
FVA30 years = $1,000,000 = C × [{[1 + (0.125/12)]30 × 12; C = $255.91 Difference = $255.91 - $72.53 = $183.38 |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 6-34 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Annuity payment |
116.
|
You have just won the lottery and will receive $540,000 as your first payment one year from now. You will receive payments for 26 years. The payments will increase in value by 4 percent each year. The appropriate discount rate is 10 percent. What is the present value of your winnings?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-37 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Growing annuity |
117.
|
You are preparing to make monthly payments of $72, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. How many payments will you have made when your account balance reaches $9,312?
t = ln 1.6467/ln 1.005; t = 100 payments |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-40 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Number of payments |
118.
|
You want to borrow $47,170 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1,160, but no more. Assume monthly compounding. What is the highest rate you can afford on a 48-month APR loan?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-41 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Interest rate |
119.
|
You need a 30-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 360-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850?
Remaining principal = $240,000 - $121,564.98 = $118,435.02 Balloon payment = $118,435.02 × [1 + (0.075/12)]30 × 12 = $1,115,840 |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 6-42 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Loan payment |
120.
|
The present value of the following cash flow stream is $5,933.86 when discounted at 11 percent annually. What is the value of the missing cash flow?
PV of missing cash flow = $5,933.86 - ($2,000/1.11) - ($1,750/1.113) - ($1,250/1.114) = $2,029.06
CF2 = $2,029.06 × 1.112 = $2,500 |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-43 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.1 Topic: Present and future values |
121.
|
You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $12,200. What is the effective annual rate on this loan?
Loan amount = $2,600,000 × 0.80 = $2,080,000
EAR = [1 + (.05797/12)]12 - 1 = 5.95 percent |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 6-45 Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.3 Topic: Effective annual rate |
122.
|
Consider a firm with a contract to sell an asset 3 years from now for $90,000. The asset costs $71,000 to produce today. At what rate will the firm just break even on this contract?
$90,000 = $71,000 × (1 + r)3; r = 8.23 percent
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 6-46 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Break-even interest |
123.
|
What is the present value of $1,100 per year, at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 30 years from now?
PV = $9,984.74/1.15 = $6,199.74 |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-47 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.2 Topic: Present value |
124.
|
You have your choice of two investment accounts. Investment A is a 5-year annuity that features end-of-month $2,500 payments and has an interest rate of 11.5 percent compounded monthly. Investment B is a 10.5 percent continuously compounded lump sum investment, also good for five years. How much would you need to invest in B today for it to be worth as much as investment A five years from now?
FVA = $2,500 × [{[1 + (0.115/12)]5 × 12 -1}/(0.115/12)] = $201,462.23
PV = $201,462.23 e-1 × 0.105 ×5 = $119,176.06 |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-49 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.3 Topic: Present value |
125.
|
Given an interest rate of 8 percent per year, what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17?
PVt = 17 = $500/.08 = $6,250
PVt = 9 = $6,250/1.0817-9 = $3,376.68 NOTE: This is a correction to the original problem solution. |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-50 Learning Objective: 06-01 How to determine the future and present value of investments with multiple cash flows. Section: 6.2 Topic: Perpetuity present value |
126.
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You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at a 6 percent APR, compounded monthly. What will your monthly payment be?
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AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 6-54 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Annuity due |
127.
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You are looking at a one-year loan of $10,000. The interest rate is quoted as 8 percent plus 5 points. A point on a loan is simply 1 percent (one percentage point) of the loan amount. Quotes similar to this one are very common with home mortgages. The interest rate quotation in this example requires the borrower to pay 5 points to the lender up front and repay the loan later with 10 percent interest. What is the actual rate you are paying on this loan?
Loan amount received = $10,000 × (1 - .05) = $9,500
Loan repayment amount = $10,000 × 1.081 = $10,800 $10,800 = $9,500 × (1 + r)1; r = 13.68 percent |
AACSB: Analytic
Blooms: Create Difficulty: 3 Hard EOC: 6-62 Learning Objective: 06-04 How interest rates are quoted (and misquoted). Section: 6.4 Topic: Effective rate with points |
128.
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Your holiday ski vacation was great, but it unfortunately ran a bit over budget. All is not lost. You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 9.4 percent. You plan to make payments of $510 a month on this debt. How many less payments will you have to make to pay off this debt if you transfer the balance to the new card?
$5,000 = $510 × [(1 - {1 + (0.094/12)]}t)/(0.094/12)] t = ln (1/0.9232)/ln 1.007833; t = 10.24 payments Difference = 10.72 - 10.24 = 0.48 payments |
AACSB: Analytic
Blooms: Analyze Difficulty: 3 Hard EOC: 6-67 Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Section: 6.2 Topic: Number of periods |
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