2.3 Teoría del aprendizaje profundo
2.3.10 Problemas del entrenamiento
1. James has just inherited $100,000. His goal is to accumulate
$200,000 in 15 years. How much of the inheritance can he spend on a car right now if the remainder will be invested at 12% compounded semiannually?
A. $34,822 B. $39,491 C. $65,178
2. Alison plans to deposit $500 in her savings account at the end of each quarter for the next 10 years. The interest rate is 10% per year
compounded quarterly. After 10 years, her account balance and the total amount of interest that she would have earned are closest to:
Account Balance Interest Earned
A. $33,701 $13,254
B. $33,701 $13,701
C. $32,504 $13,254
3. What sum should be deposited today at 8% compounded quarterly if one wants to accumulate $200,000 in 6 years? How much interest will be earned during the period?
Amount Deposited Today Interest Earned
A. $124,344 $69,788
B. $124,344 $75,656
C. $130,212 $75,656
4. If an investment of $400,000 were to grow to $5,000,000 over a period of 20 years, what is the stated annual rate at which it must be invested, given that the return is compounded semiannually?
A. 6.52%
B. 6%
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C. 13.04%
5. A company takes a loan of $200,000 at an interest rate of 12%. The loan must be paid back in 7 years through equal end-of-year annual installments. The value of principle outstanding after the second payment has been made is closest to:
A. $43,824 B. $19,824 C. $157,974
6. George is thinking of taking a loan of $50,000 to buy a house. The loan will be fully amortized with equal monthly installments over 10 years.
Given that the interest rate is 8% compounded monthly, the amount of each mortgage payment and the effective interest rate will be closest to:
Mortgage Payment Effective Interest Rate
A. $607 8.3%
B. $615 8.15%
C. $606 8.3%
7. James must bear his annual college tuition of $8,000 for 3 years, starting with the beginning of next year. How much must he invest today at 10%, compounded annually to meet his requirements? What is the balance in his account after the first withdrawal?
Amount Deposited Today
Balance After First Withdrawal
A. $19,895 $14,375
B. $19,895 $13,884
C. $20,825 $14,375
8. Martha invests $500,000 at 10% compounded annually. How many annual withdrawals of exactly $60,000 can she make assuming that withdrawals will be made at the beginning of each year starting today?
A. 13 years
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B. 14 years C. 15 years
9. An annuity pays $50,000 annually at the beginning of each year for 15 years. If the discount rate equals 8%, the present value of the annuity is closest to:
A. $462,212 B. $427,974 C. $453,294
10. What is the future value of an annuity due that pays $500 for 5 years given that the interest rate is 0%?
A. $2,500 B. $2,000
C. None of the above
11. In order to withdraw $1,000 at the beginning of each of the next 4 years, how much must an investor invest today? Assume that the annual interest rate is 9%.
A. $3,531 B. $3,240 C. $3,128
12. Which of the following is least likely a component of the required rate of return on a security after the nominal risk-free rate has been
deducted?
A. Maturity risk premium B. Default risk premium C. Inflation risk premium
13. Which of the following least likely offers a series of finite cash flows?
A. Ordinary annuity B. Annuity due C. Perpetuity
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14. A loan is amortized over time with equal annual payments. How do the principal and interest components of the annual payment change over time?
Interest Component Principal Repayment Component
A. Decreases Increases
B. Increases Decreases
C. Decreases Decreases
15. Bill wants to accumulate $15,000 in 4 years by making four equal end-of-year deposits. Given that the interest rate is 7%, what is the
minimum amount that he should deposit each year?
A. $3,378 B. $4,428 C. $3,157
16. Robert received $150,000 and invested it at 6% compounded annually.
He wants to purchase a piece of property worth $200,000 after 7 years. He will most likely:
A. Be able to purchase the property and have excess funds amounting to $25,544
B. Be able to purchase the property and have excess funds amounting to $2,554
C. Not be able to purchase the property as he will be $2,554 short.
17. If $20 invested today is worth $200 in 5 years, what is the stated annual rate of return assuming monthly compounding?
A. 58.5%
B. 46.95%
C. 45%
18. At a 100% annual interest rate, a rational investor would be indifferent between receiving $20 today and:
A. $60 after 2 years B. $30 after 1 year
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C. $160 after 3 years
19. An annuity pays $12,000 every year for 5 years with the first payment at the end of Year 4. Given a 13% discount rate, the present value of this annuity is closest to?
A. $42,207 B. $29,251 C. $28,334
20. Larry purchases a car worth $20,000 by making an initial payment of
$3,000. The rest of the amount is financed with a loan that requires equal monthly payments over 24 months. Assuming a 12% interest rate implicit in the loan, the monthly installment is closest to:
A. $800 B. $11,834 C. $2,569
21. Mary invested $3,000 in an account with an interest rate of 15%
compounded continuously. After 5 years, the value of her investment will be closest to:
A. $6,351 B. $6,030 C. $6,240
22. Which of the following is least likely a premium that compensates investors for bearing risk?
A. Default risk premium B. Maturity premium C. Payback premium
23. Which of the following statements is most accurate?
A. The longer the time period till the future amount is received, the higher its present value
B. The higher the discount rate, the higher the present value of the
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amount
C. The shorter the time period till the future amount is received, the higher its present value
24. The value of an investment of $500 forty years from today, given that it is made 3 years from now at an interest rate of 7.25% is closest to:
A. $6,663 B. $8,220 C. $7,146
25. Brian will receive $1,000 at the end of each year for the next 21 years.
Given that the interest rate is 8%, the value of these payments 43 years from today is closest to:
A. $274,126 B. $50,423 C. $55,457
26. An investor will receive $365 at the end of each year for 13 years. The first payment will be received 4 years from now. Given that the interest rate is 3%, the present value of this cash flow stream is closest to:
A. $3,552 B. $3,882 C. $3,449
27. An investment of $3,000 is made at the beginning of each of the next 7 years. Given an interest rate of 0.67%, the value of this investment 11 years from today is closest to:
A. $21,570 B. $22,154 C. $22,007
28. An investor expects to receive $79 at the beginning of each year for 3 years. The first payment will be received 5 years from today. Given a discount rate of 6%, the present value of the annuity is closest to:
A. $167.26
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B. $177.32 C. $211.13
29. A company pays a $2 per share annual dividend on its preferred stock.
Given that the required rate of return is 5% and that this dividend policy will continue forever, the value of the preferred stock today is closest to:
A. $19 B. $40 C. $55
30. Given a discount rate of 3%, the value as of the end of Year 5 of the following cash flow stream is closest to:
Year 0 −$200 Year 1 $150 Year 2 $250 Year 3 −$100 Year 4 $400 Year 5 −$75 A. $425.30
B. $441.06 C. $492.69
31. Given a discount rate of 3%, the present value of the cash flow stream presented below is closest to:
Year 0 −$1,100 Year 1 $1,500 Year 2 $750 Year 3 −$1,000 Year 4 $4,000 Year 5 −$275
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A. $3,464.85 B. $3,342.72 C. $3,875.64
32. Sarah wants to accumulate $10,000 over the next 10 years. Given a rate of return of 10%, the fixed amount that she should deposit in the bank at the end of each year for the next 10 years is closest to:
A. $657.45 B. $627.45 C. $557.45
33. An investor puts $3,000 in a bank account that offers an annual
interest rate of 11% compounded daily. The account balance at the end of Year 1 will be closest to:
A. $3,348.78 B. $3,000.10 C. $2,997.44
34. Over the next 5 years, MT Technologies expects to earn the following amounts:
Year 1 $90 million Year 2 $76 million Year 3 $92 million Year 4 $105 million Year 5 $103 million
The annually compounded growth rate based on the company’s forecasts is closest to:
A. 7.96%
B. 2.74%
C. 3.43%
35. The effective annual rate for an automobile loan that has an interest rate of 7%, compounded monthly is closest to:
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A. 7.35%
B. 7.23%
C. 8.12%
36. Sarah wants to start college after 5 years for which she wants to accumulate money by making annual deposits in her bank account beginning at the end of Year 1. She estimates that she will have to make a payment of $8,000 at the beginning of each year through the 4-year study program with the first payment to be made at the
beginning of Year 6. Given a discount rate of 11%, the amount that must be deposited at the end of each year for the next 5 years to satisfy the eventual payment obligations is closest to:
A. $3,985 B. $6,400 C. $4,424
37. Juan Carlos wants to save money for his son’s college tuition. His son will start college after 10 years and Carlos expects to make annual payments of $12,500 at the beginning of each year for a 5-year study program with the first payment to be made at the beginning of Year 11.
Given a discount rate of 12% the amount that Carlos must deposit at the end of each of the next 10 years is closest to:
A. $2,876 B. $2,568 C. $2,658
38. James must make 6 annual payments of $2,000 each starting at the beginning of Year 5. Given a discount rate of 10%, which of the following methods will enable him to make the required payments:
Method 1: Make 4 equal annual deposits of $1,800 beginning at the end of Year 1.
Method 2: Make 2 equal annual deposits of $4,600 beginning at the end of Year 3.
A. Method 1 only
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B. Method 2 only C. Both the methods
39. Sonia wants to invest $5,000 and is considering the following investments over a horizon of 8 years:
Investment 1: Invest in a mutual fund which is expected to earn 8% for the first 3 years and 12% thereafter.
Investment 2: Invest in a savings account which is expected to offer 11% a year compounded annually.
Investment 3: Invest in gold whose current value is expected to double in 8 years.
Which of these investments offers the highest return based on her expectations?
A. Investment 1 B. Investment 2 C. Investment 3
40. Martha is 30 years old and wants to retire in 20 years at the age of 50.
She expects to earn 12% on her savings prior to retirement and 8%
thereafter. Martha wants to be able to withdraw $18,000 every year at the beginning of each year for 30 years from the age of 50 to 80. The amount that she must deposit at the end of each year for the next 20 years is closest to:
A. $2,812 B. $2,724 C. $3,037
41. Susan borrowed $5,000 for renovating her home. The loan carries an interest rate of 9% and must be repaid in fixed annual end-of-year installments over the next 5 years. The interest component of the second payment is closest to:
A. $450 B. $375 C. $325
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42. Henry borrowed $12,000 to start his own business. The loan must be repaid through four equal end-of-year payments and carries an
interest rate of 8%. The principal component of the second payment is closest to:
A. $2,876 B. $2,663 C. $3,623
43. Mrs. Doherty wants to gift a car worth $24,000 to her son for his 18th birthday. She has 40% of the funds, and borrows the rest for 4 years at 8% compounded monthly. The fixed monthly payment that she will have to make to retire the loan in 48 months is closest to:
A. $286 B. $234 C. $352
44. William is evaluating the following options for investing $10,000 for 5 years:
Investment A: Offers a 10% interest rate compounded monthly.
Investment B: Offers a 12% interest rate compounded semi-annually.
Investment C: Offers an 11% interest rate compounded quarterly.
Which of the following statements is most accurate?
A. Investment A offers $1,455 less than Investment B.
B. Investment C offers a $704 greater return than Investment B.
C. Investment A offers a $751 greater return than Investment C.
45. Given a discount rate of 11%, which of the following cash flow streams has the highest present value?
A. 12 equal payments of $600 beginning at the end of Year 1.
B. 10 equal payments of $600 beginning immediately.
C. 12 equal payments of $550 beginning immediately.
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Reading 5: The Time Value of Money
1. James has just inherited $100,000. His goal is to accumulate
$200,000 in 15 years. How much of the inheritance can he spend on a car right now if the remainder will be invested at 12% compounded semiannually?
A. $34,822 B. $39,491 C. $65,178 Answer: C
FV = −200,000; I/Y = 12%/2 = 6; N = (15)(2) = 30; CPT PV; PV =
$34,822.03
Amount that he can spend in the current period = $100,000 −
$34,822 = $65,178
2. Alison plans to deposit $500 in her savings account at the end of each quarter for the next 10 years. The interest rate is 10% per year
compounded quarterly. After 10 years, her account balance and the total amount of interest that she would have earned are closest to:
Account Balance Interest Earned
A. $33,701 $13,254
B. $33,701 $13,701
C. $32,504 $13,254
Answer: B
PMT = −$500; N = (10)(4) = 40; I/Y = 10%/4 = 2.5; PV = 0; CPT FV;
FV = Account balance after 10 years = $33,701.28
Over the period she will make 40 deposits worth $500 each for a total of $20,000
Therefore, total interest income = $33,701 − $20,000 = $13,701
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3. What sum should be deposited today at 8% compounded quarterly if one wants to accumulate $200,000 in 6 years? How much interest will be earned during the period?
Amount Deposited Today Interest Earned
A. $124,344 $69,788
B. $124,344 $75,656
C. $130,212 $75,656
Answer: B
I/Y = 8/4 = 2%; N = (6)(4) = 24; FV = −$200,000; CPT PV; PV =
$124,344
Interest earned = FV – PV = $200,000 − $124,344 = $75,656 4. If an investment of $400,000 were to grow to $5,000,000 over a
period of 20 years, what is the stated annual rate at which it must be invested, given that the return is compounded semiannually?
A. 6.52%
B. 6%
C. 13.04%
Answer: C
PV = −$400,000; FV = $5,000,000; N = (20)(2) = 40; CPT I/Y;
I/Y = Semiannual discount rate = 6.52%.
Stated annual rate = 6.52 × 2 = 13.04%
5. A company takes a loan of $200,000 at an interest rate of 12%. The loan must be paid back in 7 years through equal end-of-year annual installments. The value of principle outstanding after the second payment has been made is closest to:
A. $43,824 B. $19,824 C. $157,974 Answer: C
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PV = $200,000; N = 7; I/Y = 12; CPT PMT; PMT = $43,823.55 Amortization table
Year Balance Interest Payment Principal Repaid
End Balance 1 $200,000 $24,000.0 $43,823.55 $19,823.6 $180,176.5 2 $180,176.5 $21,621.2 $43,823.55 $22,202.4 $157,974.09 An easier way to solve this question is to simply compute the PV of the remaining payments at the end of Year 2.
N = 5; I/Y = 12; PMT = −$43,823.55; CPT PV; PV = $157,974.09
6. George is thinking of taking a loan of $50,000 to buy a house. The loan will be fully amortized with equal monthly installments over 10 years.
Given that the interest rate is 8% compounded monthly, the amount of each mortgage payment and the effective interest rate will be closest to:
Mortgage Payment Effective Interest Rate
A. $607 8.3%
B. $615 8.15%
C. $606 8.3%
Answer: A
PV = $50,000; N = 120; I/Y = 8/12 = 0.67; CPT PMT; PMT = $606.74 Effective interest rate = [(1 + 0.006667)12] – 1 = 0.083 or 8.3% OR you could use the Interest conversion function on your BA II Plus:
[2ND][2] to enter the ICONV function [2ND][CE|C] to clear memory
[8][ENTER] enter the nominal interest rate
[↓][↓][12][ENTER] enter the compounding periods per year C/Y [↑][CPT] compute the effective interest rate
7. James must bear his annual college tuition of $8,000 for 3 years,
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starting with the beginning of next year. How much must he invest today at 10%, compounded annually to meet his requirements? What is the balance in his account after the first withdrawal?
Amount Deposited Today
Balance After First Withdrawal
A. $19,895 $14,375
B. $19,895 $13,884
C. $20,825 $14,375
Answer: B
He needs to make the first withdrawal at the beginning of next year (or at the end of this year) at t = 1
N = 3; PMT = −$8,000; I/Y = 10; CPT PV; PV = $19,894.82 At the end of Year 1, the balance in his account is calculated as:
N = 2; PMT = −$8,000; I/Y = 10; CPT PV; PV = $13,884.29
8. Martha invests $500,000 at 10% compounded annually. How many annual withdrawals of exactly $60,000 can she make assuming that withdrawals will be made at the beginning of each year starting today?
A. 13 years B. 14 years C. 15 years Answer: B
Switch your calculator to BGN mode.
PV = −$500,000; I/Y = 10; PMT = $60,000; CPT N; N = 14.86 years.
Therefore, 14 withdrawals of $60,000 can be made (the 15th withdrawal will be less than $60,000).
Note: The signs of PMT and PV must be different.
9. An annuity pays $50,000 annually at the beginning of each year for 15 years. If the discount rate equals 8%, the present value of the annuity is closest to:
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A. $462,212 B. $427,974 C. $453,294 Answer: A
Switch your calculator to BGN mode.
PMT = −$50,000; I/Y = 8; N = 15; CPT PV; PV = $462,211.85
10. What is the future value of an annuity due that pays $500 for 5 years given that the interest rate is 0%?
A. $2,500 B. $2,000
C. None of the above Answer: A
Since the interest rate is 0%, the PV and FV of the payments are equal.
The annuity is simply worth the sum of all the payments. $500 × 5 =
$2,500
11. In order to withdraw $1,000 at the beginning of each of the next 4 years, how much must an investor invest today? Assume that the annual interest rate is 9%.
A. $3,531 B. $3,240 C. $3,128 Answer: A
Switch your calculator to BGN mode.
PMT = −$1,000; N = 4; I/Y = 9; CPT PV; PV = $3,531
12. Which of the following is least likely a component of the required rate of return on a security after the nominal risk-free rate has been
deducted?
A. Maturity risk premium B. Default risk premium
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C. Inflation risk premium Answer: C
The required rate of return is the sum of nominal risk-free rate of return (which includes the real risk-free rate of return and an
inflation premium), maturity risk premium, default risk premium, and liquidity risk premium.
13. Which of the following least likely offers a series of finite cash flows?
A. Ordinary annuity B. Annuity due C. Perpetuity Answer: C
A perpetuity offers a series of cash flows that go on forever.
14. A loan is amortized over time with equal annual payments. How do the principal and interest components of the annual payment change over time?
Interest Component Principal Repayment Component
A. Decreases Increases
B. Increases Decreases
C. Decreases Decreases
Answer: A
The payments made over time reduce the outstanding principal amount. Therefore, the interest component decreases with each payment. Since all payments are equal, a reduction in the interest component implies an increase in the principal repayment component.
15. Bill wants to accumulate $15,000 in 4 years by making 4 equal end-of-year deposits. Given that the interest rate is 7%, what is the minimum amount that he should deposit each year?
A. $3,378 B. $4,428 C. $3,157
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Answer: A
FV = $15,000; I/Y = 7; N = 4; CPT PMT; PMT= −$3,378.
Note: Your calculator must be in END mode.
16. Robert received $150,000 and invested it at 6% compounded annually.
He wants to purchase a piece of property worth $200,000 after 7 years. He will most likely:
A. Be able to purchase the property and have excess funds amounting to $25,544
B. Be able to purchase the property and have excess funds amounting to $2,554
C. Not be able to purchase the property as he will be $2,554 short Answer: A
PV = $150,000; N = 7; I/Y = 6; CPT FV; FV= −$225,544.
Therefore, he will be able to buy the property for $200,000 and still save $25,544.
17. If $20 invested today is worth $200 in 5 years, what is the stated annual rate of return assuming monthly compounding?
A. 58.5%
B. 46.95%
C. 45%
Answer: B
PV = −$20; N = 5 × 12 = 60; FV = $200; CPT I/Y; I/Y = 3.9122%
Rate of return = 3.9122 × 12 = 46.95%
Note: PV and FV must have opposite signs.
18. At a 100% annual interest rate, a rational investor would be indifferent between receiving $20 today and:
A. $60 after 2 years B. $30 after 1 year C. $160 after 3 years
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Answer: C
At an interest rate of 100%, $20 will be worth $40 in 1 year, $80 in 2 years, and $160 in 3 years.
19. An annuity pays $12,000 every year for 5 years with the first payment at the end of Year 4. Given a 13% discount rate, the present value of this annuity is closest to?
A. $42,207 B. $29,251 C. $28,334 Answer: B
To solve this problem, we first find the present value (at the end of Year 3) of the 5- year annuity, and then discount it for another 3 years to compute its PV today.
Step 1: PMT = −$12,000; N = 5; I/Y = 13; CPT PV; PV = −$42,206.77 Step 2: FV = −$42,206.77; N = 3; I/Y = 13; CPT PV; PV = $29,251.41 20. Larry purchases a car worth $20,000 by making an initial payment of
$3,000. The rest of the amount is financed with a loan that requires equal monthly payments over 24 months. Assuming a 12% interest rate implicit in the loan, the monthly installment is closest to:
A. $800 B. $11,834 C. $2,569 Answer: A
An amount of $17,000 has to be paid back over the next 2 years.
I/Y = 12/12 = 1; N = 12 × 2 = 24; PV = −$17,000, CPT PMT; PMT =
I/Y = 12/12 = 1; N = 12 × 2 = 24; PV = −$17,000, CPT PMT; PMT =