Problem Set 1 Compound Interest Problems

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					Problem Sets                              FINA 3770-004                                    Spring 2005


                    Problem Set 1: Compound Interest Problems
Prior to attempting problems 1-37, please review examples 1, 2, 3, 4, and 5 of Lecture Topic 4.
1. Suppose you invest $1,000 on January 31, 2005, earning 10% compounded annually. How
     much will you have on January 31, 2015?
2. Suppose you invest $1,000 on January 31, 2005, earning 10% compounded semi-annually.
     How much will you have on January 31, 2015?
3. At 10% compounded quarterly, what will $1,000 grow to in 10 years?
4. At 10% compounded continuously, what will $1,000 grow to in 10 years?
5. At 12% compounded annually, what will $1,000 grow to in 10 years?
6. At 12% compounded semi-annually, what will $1,000 grow to in 10 years?
7. At 12% compounded quarterly, what will $1,000 grow to in 10 years?
8. At 12% compounded monthly, what will $1,000 grow to in 10 years?
9. At 12% compounded continuously, what will $1,000 grow to in 10 years?
10. At 9% compounded annually, what will $1,000 grow to in 10 years?
11. At 9% compounded semi-annually, what will $1,000 grow to in 10 years?
12. At 9% compounded monthly, what will $1,000 grow to in 10 years?
13. At 9% compounded continuously, what will $1,000 grow to in 10 years?
14. What is the effective rate that is equivalent to 10% compounded semi-annually?
15. What is the effective rate that is equivalent to 10% compounded quarterly?
16. What is the effective rate that is equivalent to 10% compounded continuously?
17. What is the effective rate that is equivalent to 12% compounded semi-annually?
18. What is the effective rate that is equivalent to 12% compounded quarterly?
19. What is the effective rate that is equivalent to 12% compounded monthly?
20. What is the effective rate that is equivalent to 12% compounded continuously?
21. What is the effective rate that is equivalent to 9% compounded quarterly?
22. What is the effective rate that is equivalent to 9% compounded monthly?
23. What is the effective rate that is equivalent to 9% compounded continuously?
Notice that as the interest rate increases, the future value (not surprisingly) also increases. At a
given annualized interest rate, the future value increases as the number of compounding periods
per year increases.
24. Suppose you can earn 10% interest compounded annually. How much would you need to
     invest today (assume it’s January 31, 2005) in order to have $1,000 on January 31,
     2013?
25. Suppose you can earn 10% interest compounded semi-annually. How much would you need
     to invest today January 31, 2005) in order to have $1,000 on January 31, 2013?
26. At 10% interest compounded quarterly, what is the present value of $1,000 to be received 8
     years from now?




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Problem Sets                             FINA 3770-004                                  Spring 2005

27. At 10% interest compounded continuously, what is the present value of $1,000 to be received 8
     years from now?
28. At 12% interest compounded annually, what is the present value of $1,000 to be received 8
     years from now?
29. At 12% interest compounded semi-annually, what is the present value of $1,000 to be received
     8 years from now?
30. At 12% interest compounded quarterly, what is the present value of $1,000 to be received 8
     years from now?
31. At 12% interest compounded monthly, what is the present value of $1,000 to be received 8
     years from now?
32. At 12% interest compounded continuously, what is the present value of $1,000 to be received 8
     years from now?
33. At 9% interest compounded annually, what is the present value of $1,000 to be received 8 years
     from now?
34. At 9% interest compounded monthly, what is the present value of $1,000 to be received 8 years
     from now?
35. At 9% interest compounded continuously, what is the present value of $1,000 to be received 8
     years from now?
36. Now, duplicate some of these using the effective rates you computed earlier, in order to prove
     to yourself that you get the same answer either way.
37. How much must you deposit now at 6% compounded quarterly in order to have $1,000 in 5
     years?
Notice that as the interest rate goes up, the present value goes down, and vice versa. Also, at a
given annualized interest rate, the present value decreases as the number of compounding periods
per year increases. That is, the more frequent the compounding, the higher the effective rate.
Prior to attempting problems 38-40 please review example 6 of Lecture Topic 4.
38. An opportunity offers to double your investment in 12 years. What rate of annually
     compounded interest is implied?
39. A house purchased for $40,000 in 1975 sold for $85,000 in 1985. What was the average
     compound annual rate of appreciation?
40. If you can earn 10% interest compounded monthly, how long will it take for an investment of
    $1,000 to grow into $2,000?
Prior to attempting problems 41-46 please review example 9 of Lecture Topic 4.
41. If inflation averages 3% per year, what will a dollar stuffed into the mattress be worth in 25
    years?
42. If inflation averages 3% per year, what will a dollar stuffed into the mattress be worth in 50
    years?
43. A dollar at the end of 1976 could purchase about as much as 58 cents could at the end of 1967.
    What was the average annually compounded inflation rate over that period?
44. If it seems to you that everything costs four times as much now as it did twenty years ago, are
    you surprised? What average annually compounded rate of inflation is implied?
45. One hundred years ago an unskilled laborer earned $1 a day. Now such a laborer earns $32 (at
    about $4 an hour for 8 hours). What is the average compound annual rate of wage inflation?


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Problem Sets                              FINA 3770-004                                   Spring 2005

46. If this rate of inflation continues, what will the daily wage be after another hundred years?
Prior to attempting problems 47-51 please review example 10 of Lecture Topic 4.
47. Suppose there is deflation of 10% annually (that is, prices drop at an annually compounded rate
    of 10%). What would a dollar stuffed into the mattress be worth in 1 year?
48. With deflation of 10% compounded annually, what would a dollar stuffed into the mattress be
    worth in 5 years?
49. With deflation of 10% compounded annually, what would a dollar stuffed into the mattress be
    worth in 10 years?
50. With deflation of 5% compounded annually, what would a dollar stuffed into the mattress be
    worth in 5 years?
51. With deflation of 5% compounded annually, what would a dollar stuffed into the mattress be
    worth in 10 years?
Prior to attempting problems 52-59 please review examples 11 & 12 of Lecture Topic 4.
52. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 3% compounded annually and the expected rate of inflation is 5% compounded
    annually?
53. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 3% compounded annually and the expected rate of inflation is 7% compounded
    annually?
54. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 4% compounded annually and the expected rate of inflation is 6% compounded
    annually?
55. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 4% compounded annually and the expected rate of inflation is 8% compounded
    annually?
56. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 5% compounded annually and the expected rate of inflation is 7% compounded
    annually?
57. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 5% compounded annually and the expected rate of inflation is 9% compounded
    annually?
58. What is the present value of $1,000 to be received 10 years from now if the required real rate of
    return is 5% compounded continuously and the expected rate of inflation is 7% compounded
    continuously?
59. What is the nominal rate in each of the seven preceding problems?
Notice that for a given real rate, the spread between the real rate and the nominal rate exceeds the
rate of inflation (except in the case of continuous compounding). This excess increases as inflation
increases.
Prior to attempting problems 60-72, please review examples 13 & 14 of Lecture Topic 4.
60. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 10% compounded annually and the
    inflation rate is expected to be 8% compounded annually?




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Problem Sets                             FINA 3770-004                                   Spring 2005

61. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 5% compounded annually and the
    inflation rate is expected to be 3% compounded annually?
62. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 8% compounded annually and the
    inflation rate is expected to be 5% compounded annually?
63. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 12% compounded annually and the
    inflation rate is expected to be 9% compounded annually?
64. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 20% compounded annually and the
    inflation rate is expected to be 16% compounded annually?
65. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 6% compounded annually and the
    inflation rate is expected to be 2% compounded annually?
66. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 6% compounded continuously and the
    inflation rate is expected to be 2% compounded continously?
67. In terms of today's purchasing power, how much would you expect to have in 10 years as the
    result of investing $1,000 today, if the nominal return is 8% compounded annually and the
    inflation rate is expected to be 10% compounded annually?
68. Calculate the real rate for each of the previous eight problems.
Notice that even with the same spread between the nominal rate and the rate of inflation, the real
rate is higher when inflation is lower.
69. If you borrow money to buy durable goods at an interest rate of 12% and inflation is 9%, what
    is the real rate of interest you are paying?
70. If you borrow money to buy durable goods at an interest rate of 9% and inflation is 5%, what is
    the real rate of interest you are paying?
71. If you borrow money to buy durable goods at an interest rate of 12% and deflation is 9%, what
    is the real rate of interest you are paying?
72. If you borrow money to buy durable goods at an interest rate of 10% and deflation is 5%, what
    is the real rate of interest you are paying?
Prior to attempting problem 73, please review example 15 of Lecture Topic 4.
73. You must decide whether to borrow money to buy a car now, or save your money and pay cash
    later. You expect car prices to be rising at about 4% per year. The best savings opportunity
    you can think of is a money market CD that you expect will earn a return of 3% per year. You
    can get a car loan at 5%. If you borrowed the money, what would be the real interest rate, after
    tax, if you are in the 25% marginal tax bracket and can deduct the interest as a business
    expense? Should you buy or wait? Assume annual compounding throughout, including the
    inflation.
74. A parcel of land purchased for $500,000 in 1974 sold for $2,500,000 in 2004. Assume that
    over this period inflation averaged 6% compounded annually. What was the average compound
    annual real rate of change in the value of this land?
75. What sort of people (or institutions) would prefer higher-than-anticipated inflation, those with
    more debts than assets or those with more assets that debts?
76. During times when inflation is higher than anticipated, which would be more valuable, money in
    the bank or productive skills?


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Fina 3770-004               SOLUTIONS: PROBLEM SET 1                              Spring 2005


1.    Data input: PV is –1000, I/YR is 10, P/YR     17. Reff = (1.06)2 – 1 = 12.36%
      is 1, N is 10, PMT is 0, compute FV.          18. Reff = (1.03)4 – 1 = 12.55%
      Result is $2,593.74
                                                    19. Reff = (1.01)1 2 – 1 = 12.68%
2.    Data input is the same as the previous
      problem, except that P/YR is 2 and N is       20. Reff = e0.12 – 1 = 12.75%
      20. FV is $2,653.30                           21. Reff = (1 + 0.09/4)4 – 1 = 9.31%
3.    Data input is the same as the previous        22. Reff = (1 + 0.09/12)1 2 – 1 = 9.38%
      problem, except that P/YR is 4 and N is
      40. FV is $2,685.06                           23. Reff = e0.09 – 1 = 9.42%
4.    Type 0.1 and multiply times 10 (annual        24. Data input: FV is 1000, I/YR is 10, P/YR
      interest multiplied by amount of time).           is 1, N is 8, PMT is 0, compute PV.
      Then press the ex button, and multiply            Result is $466.51. The negative sign in
      times 1000. The result is $2,718.28               the display indicates that you must make
                                                        an investment (outflow of funds) in time
5.    Data input: PV is –1000, I/YR is 12, P/YR         zero, in order to receive an inflow in the
      is 1, N is 10, PMT is 0, compute FV.              future.
      Result is $3,105.85
                                                    25. Data input is the same as the previous
6.    Data input is the same as the previous            problem, except that P/YR is 2 and N is
      problem, except that P/YR is 2 and N is           16. PV is $458.11
      20. FV is $3,207.14
                                                    26. Data input is the same as the previous
7.    Data input is the same as the previous            problem, except that P/YR is 4 and N is
      problem, except that P/YR is 4 and N is           32. PV is $453.77
      40. FV is $3,262.04
                                                    27. Type –0.1 and multiply times 8 (annual
8.    Data input is the same as the previous            interest multiplied by amount of time, with
      problem, except that P/YR is 12 and N is          negative sign). Then press the ex button,
      120. FV is $3,300.39                              and multiply times 1000. The result is
9.    Type 0.12 and multiply times 10 (annual           $449.33
      interest multiplied by amount of time).       28. Data input: FV is 1000, I/YR is 12, P/YR
      Then press the ex button, and multiply            is 1, N is 8, PMT is 0, compute PV.
      times 1000. The result is $3,320.12               Result is $403.88. The negative sign in
10.   Data input: PV is –1000, I/YR is 9, P/YR          the display indicates that you must make
      is 1, N is 10, PMT is 0, compute FV.              an investment (outflow of funds) in time
      Result is $2,367.36                               zero, in order to receive an inflow in the
                                                        future.
11.   Data input is the same as the previous
      problem, except that P/YR is 2 and N is       29. Data input is the same as the previous
      20. FV is $2,411.71                               problem, except that P/YR is 2 and N is
                                                        16. PV is $393.65
12.   Data input is the same as the previous
      problem, except that P/YR is 12 and N is      30. Data input is the same as the previous
      120. FV is $2,451.36                              problem, except that P/YR is 4 and N is
                                                        32. PV is $388.34
13.   Type 0.09 and multiply times 10 (annual
      interest multiplied by amount of time).       31. Data input is the same as the previous
      Then press the ex button, and multiply            problem, except that P/YR is 12 and N is
      times 1000. The result is $2,459.60               96. PV is $384.72
14.     Reff = (1.05)2 – 1 = 10.25%                 32. Type –0.12 and multiply times 8 (annual
                                                        interest multiplied by amount of time, with
15.     Reff = (1.025)4 – 1 = 10.38%                    negative sign). Then press the ex button,
16.     Reff = e0.1 – 1 = 10.52%                        and multiply times 1000. The result is
                                                        $382.89


                                           page 5
Fina 3770-004              SOLUTIONS: PROBLEM SET 1                                Spring 2005


33. Data input: FV is 1000, I/YR is 9, P/YR is      43. Data input: Fat Value (FV) is 1, Puny
    1, N is 8, PMT is 0, compute PV. Result             Value (PV) is –0.58, P/YR is 1, N is 9,
    is $501.87. The negative sign in the                PMT is 0, compute I/YR. Result is
    display indicates that you must make an             6.24%. (The negative sign for PV
    investment (outflow of funds) in time               recognizes the sign convention).
    zero, in order to receive an inflow in the      44. Data input: Fat Value (FV) is 4, Puny
    future.                                             Value (PV) is –1, P/YR is 1, N is 20,
34. Data input is the same as the previous              PMT is 0, compute I/YR. Result is
    problem, except that P/YR is 12 and N is            7.18%. (The negative sign for PV
    96. PV is $488.06                                   recognizes the sign convention).
35. Type –0.09 and multiply times 8 (annual         45. Data input: Fat Value (FV) is 32, Puny
    interest multiplied by amount of time, with         Value (PV) is –1, P/YR is 1, N is 100,
    negative sign). Then press the ex button,           PMT is 0, compute I/YR. Result is
    and multiply times 1000. The result is              3.53%. (The negative sign for PV
    $486.75                                             recognizes the sign convention).
36. Answers should agree exactly. Errors            46. Leave data from the previous problem,
    result from rounding the effective rate.            except that PV is –32. Then compute FV.
    Even a small difference between the exact           Result is $1,024
    effective rate and the rounded version can      47. Data input: FV is 1, P/YR is 1, N is 1,
    throw off the calculation by a surprising           PMT is 0, I/YR is –10, compute PV. The
    extent.                                             result tells us that $1 to be received a year
37. Data input: FV is 1000, I/YR is 6, P/YR is          from now would purchase as much as
    4, N is 20, PMT is 0, compute PV. Result            $1.11 does today. (The negative sign for
    is $742.47. The negative sign in the                PV recognizes the sign convention).
    display indicates that you must make an         48. Data input is the same as the previous
    investment (outflow of funds) in time               problem, except that N is 5. The result
    zero, in order to receive an inflow in the          tells us that $1 five years from now would
    future.                                             purchase as much as $1.69 does today.
38. PV is –1 and FV is 2. P/YR is 1 and n is            (The negative sign for PV recognizes the
    12. Calculate I/YR. Result is 5.95%                 sign convention).
39. PV is –40,000 and FV is 85,000. P/YR is         49. Data input is the same as the previous
    1 and n is 10. Calculate I/YR. Result is            problem, except that N is 10. The result
    7.83%                                               tells us that $1 ten years from now would
                                                        purchase as much as $2.87 does today.
40. P/YR is 12, PV is –1000, FV is 2000,                (The negative sign for PV recognizes the
    I/YR is 10. You will find n is almost 84            sign convention).
    months (7 years), so it would take 7 years
    to pass the goal. After 83 months you           50. Data input is the same as the previous
    would have $1991.33, and after 84                   problem, except that I/YR is –5 and N is
    months you would be across the goal line            5. The result tells us that $1 five years
    with $2007.92                                       from now would purchase as much as
                                                        $1.29 does today. (The negative sign for
41. Data input: Fat Value (FV) is 1, I/YR is 3,         PV recognizes the sign convention).
    P/YR is 1, N is 25, PMT is 0, compute
    Puny Value (PV). Result is 48¢. (The            51. Data input is the same as the previous
    negative sign in the display is due to the          problem, except that N is 10. The result
    sign convention).                                   tells us that $1 ten years from now would
                                                        purchase as much as $1.67 does today.
42. Data input is the same as the previous              (The negative sign for PV recognizes the
    problem, except that and N is 50. PV is             sign convention).
    23¢.



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Fina 3770-004              SOLUTIONS: PROBLEM SET 1                               Spring 2005


52. This can be done in one step using the          57. Data input is the same as the previous
    nominal rate. Data input follows: FV is             problem, except that the nominal rate is
    1000, P/YR is 1, I/YR is 8.15, N is 10,             14.45 (if you do the one-step method).
    PMT is 0, compute PV. Result is                     Result is $259.32. (The negative sign for
    $456.81. (The negative sign for PV                  PV recognizes the sign convention).
    recognizes the sign convention).                    For the two-step method I/YR is 9 in the
    Alternatively, the calculation can be done          first step, and 5 in the second step.
    in two steps. First deflate the future          58. This can be done in one step using the
    amount, as follows: Fat Value (FV) is               nominal rate, 7% + 5% = 12%
    1000, P/YR is 1, I/YR is 5, N is 10, PMT            (remember, the Fisher Effect simplifies
    is 0, compute Puny Value (PV).                      with continuous compounding). Type
    Intermediate result is –631.91. Second              –0.12 and multiply times 10 (annual
    step: change sign to positive, input as FV,         inflation multiplied by amount of time).
    change I/YR to 3, and compute PV. Final             Then press the ex button, and multiply
    result is $456.81. (The negative sign for           times 1000. Result is $301.19
    PV recognizes the sign convention).
                                                        Alternativey, the calculation can be done
53. Data input is the same as the previous              in two steps. First deflate the future
    problem, except that the nominal rate is            amount, as follows: Type –0.07 and
    10.21 (if you do the one-step method).              multiply times 10 (annual inflation
    Result is $378.26. (The negative sign for           multiplied by amount of time). Then
    PV recognizes the sign convention).                 press the ex button, and multiply times
    For the two-step method I/YR is 7 in the            1000. Intermediate result is $469.59.
    first step, and 3 in the second step.               Store this in one of the memory registers.
                                                        Second step: Type –0.05 and multiply
54. Data input is the same as the previous              times 10 (annual real rate multiplied by
    problem, except that the nominal rate is            amount of time). Then press the ex
    10.24 (if you do the one-step method).              button, and multiply times the amount
    Result is $377.23. (The negative sign for           stored in memory. Final result is
    PV recognizes the sign convention).                 $301.19
    For the two-step method I/YR is 6 in the        59. This problem is included in the set in
    first step, and 4 in the second step.               order to make sure everyone can find the
55. Data input is the same as the previous              nominal rates, even those who choose to
    problem, except that the nominal rate is            do the calculations using the two-step
    12.32 (if you do the one-step method).              approach. To find the nominal rate, first
    Result is $312.92. (The negative sign for           add the real rate to the rate of inflation,
    PV recognizes the sign convention).                 then add the product of the two. The
                                                        nominal rates are as follows: 8.15%,
    For the two-step method I/YR is 8 in the            10.21%, 10.24%, 12.32%, 12.35%,
    first step, and 4 in the second step.               14.45%, 12.00%
56. Data input is the same as the previous
    problem, except that the nominal rate is
    12.35 (if you do the one-step method).
    Result is $312.08. (The negative sign for
    PV recognizes the sign convention).
    For the two-step method I/YR is 7 in the
    first step, and 5 in the second step.




                                           page 7
Fina 3770-004               SOLUTIONS: PROBLEM SET 1                               Spring 2005


60. This calculation can be done in two steps.       66. This calculation can be done in two steps.
    First find the future amount, as follows:            First find the future amount, as follows:
    PV is –1000, P/YR is 1, I/YR is 10, N is             Type 0.06 and multiply times 10 (annual
    10, PMT is 0, compute FV. Intermediate               interest multiplied by amount of time).
    result is $2,593.74. Second step: change             Then press the ex button, and multiply
    I/YR to 8, and compute PV. Final result              times 1000. Intermediate result is
    is $1,201.40                                         $1,822.12. Store this in one of the
                                                         memory registers. Second step: Type
    Now you can find the real return as                  –0.02 and multiply times 10 (annual
    follows: change sign in the display to               interest multiplied by amount of time).
    positive and input as FV. Then PV is                 Final result is $1,491.82
    –1000; compute I/YR. Result is
    approximately 1.85%                                  Altenatively, the calculation can be done in
                                                         one step, using the real rate, 6% – 2% =
61. Data input is the same as the previous               4%. Then type 0.04 and multiply times
    problem, except that I/YR is 5 in the first          10 (annual interest multiplied by amount
    step, and 3 in the second step. Final result         of time). Then press the ex button, and
    is $1,212.05                                         multiply times 1000. Result is $1,491.82
    You can find the real return the same way        67. This calculation can be done in two steps.
    as in the previous problem. The result is            First find the future amount, as follows:
    approximately 1.94%                                  PV is –1000, P/YR is 1, I/YR is 8, N is 10,
62. Data input is the same as the previous               PMT is 0, compute FV. Intermediate
    problem, except that I/YR is 8 in the first          result is $2,158.92. Second step: change
    step, and 5 in the second step. Final result         I/YR to 10, and compute PV. Final result
    is $1,325.39                                         is $832.36.
    You can find the real return the same way            Now you can find the real return as
    as in the previous problem. The result is            follows: change sign in the display to
    approximately 2.86%                                  positive and input as FV. Then PV is
                                                         –1000; compute I/YR. The result is
63. Data input is the same as the previous               negative, approximately –1.82%
    problem, except that I/YR is 12 in the first
    step, and 9 in the second step. Final result     68. Approximate real rates are given with the
    is $1,311.94                                         solutions above.
    You can find the real return the same way        69. R = (0.12 – 0.09)/1.09 ≈ 2.75%
    as in the previous problem. The result is
    approximately 2.75%                              70.   R = (0.09 – 0.05)/1.05 ≈ 3.81%
64. Data input is the same as the previous           71.   R = (0.12 – (– 0.09))/(1–.09) ≈ 23.08%
    problem, except that I/YR is 20 in the first     72.   R = (0.10 – (– 0.05))/(1–.05) ≈ 15.79%
    step, and 16 in the second step. Final
    result is $1,403.57
    You can find the real return the same way
    as in the previous problem. The result is
    approximately 3.45%
65. Data input is the same as the previous
    problem, except that I/YR is 6 in the first
    step, and 2 in the second step. Final result
    is $1,469.12
    You can find the real return the same way
    as in the previous problem. The result is
    approximately 3.92%



                                            page 8
Fina 3770-004               SOLUTIONS: PROBLEM SET 1   Spring 2005


73. Nominal rate after tax is 5% times 0.75 =
    3.75%. Then subtract inflation, leaving a
    negative result, –0.25%. Finally, divide
    this by 1.04 (one plus the rate of
    inflation), for a result of approximately
    –0.24%
    The real rate of interest for borrowing is
    negative after tax. Furthermore, the after-
    tax real return from investing in the CD
    would be negative, so borrow the money
    and buy the car now.
74. Easiest approach is to deflate the selling
    price, then calculate rate of return. So in
    the, FV is 2,500,000, N is 30, I/YR is 6,
    P/YR is 1, PMT is 0, compute PV and
    obtain $435,275.33. Second step: change
    the sign in the display to positive and
    enter this result as FV. PV is –500000,
    compute I/YR. The result is –0.46%,
    indicating that in real terms you lost
    money on this investment.
    Or, you could inflate the purchase price
    and then calculate rate of return. Then in
    the first step, PV is 500,000, N is 30, I is
    6%, P/YR is 1, PMT is 0, compute FV
    and obtain $2,871,745.59. For the
    second step change the sign to negative
    and enter this result as PV, input the sales
    price of 2,500,000 as FV, and compute
    interest (don’t forget the sign
    convention—either PV or FV must be
    negative). The answer again is –0.46%,
    indicating that in real terms you lost
    money on this investment.
    Another alternative is to calculate the
    nominal rate and plug it into the Fisher
    effect calculation. Then in the first step,
    FV is 2,500,000, PV is –500,000, N is 30,
    P/YR is 1, PMT is 0, compute interest.
    The result is approximately 5.51%. Next,
    subtract 6% and divide by 1.06. The
    answer again is –0.46%.

75.   More debt than assets

76.   Skills




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