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CHAPTER 6 - 21
48. The time line is:
49. The time line for the annuity is:
CHAPTER 6 - 22
50. The time line is:
51. The time line is:
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52. The time line is:
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53. a. If the payments are in the form of an ordinary annuity, the present value will be:
54. The time line is:
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Using this equation:
55. The payment for a loan repaid with equal payments is the annuity payment with the loan value as the
PV of the annuity. So, the loan payment will be:
56. This amortization table calls for equal principal payments of $12,600 per year. The interest payment
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Challenge
57. The time line is:
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58. To answer this question, we should find the PV of both options, and compare them. Since we are
purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the
CHAPTER 6 - 28
59. To find the quarterly salary for the player, we first need to find the PV of the current contract. The
cash flows for the contract are annual, and we are given a daily interest rate. We need to find the EAR
so the interest compounding is the same as the timing of the cash flows. The EAR is:
60. The time line is:
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61. The time line is:
62. Again, to find the interest rate of a loan, we need to look at the cash flows of the loan. Since this loan
is in the form of a lump sum, the amount you will repay is the FV of the principal amount, which will
be:
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63. This is the same question as before, with different values. So:
64. First we will find the APR and EAR for the loan with the refundable fee. Remember, we need to use
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65. The time line is:
66. Here we are solving a two-step time value of money problem. Each question asks for a different
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The required savings each year will be:
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67. We will calculate the number of periods necessary to repay the balance with no fee first. We simply
need to use the PVA equation and solve for the number of payments.
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Note that we do not need to calculate the time necessary to repay your current credit card with a fee
68. We need to find the FV of the premiums to compare with the cash payment promised at age 65. We
have to find the value of the premiums at year 6 first since the interest rate changes at that time. So:
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69. The monthly payments with a balloon payment loan are calculated assuming a longer amortization
schedule, in this case, 30 years. The payments based on a 30-year repayment schedule would be:
70. Here we need to find the interest rate that makes the PVA, the college costs, equal to the FVA, the
savings. The PV of the college costs are:
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71. Here we need to find the interest rate that makes us indifferent between an annuity and a perpetuity.
To solve this problem, we need to find the PV of the two options and set them equal to each other. The
PV of the perpetuity is:
72. The cash flows in this problem occur every two years, so we need to find the effective two-year rate.
One way to find the effective two-year rate is to use an equation similar to the EAR, except use the
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73. To solve for the PVA due:
74. We need to find the lump sum payment into the retirement account. The present value of the desired
amount at retirement is:
75. a. The APR is the interest rate per week times 52 weeks in a year, so:
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c. Using the cash flows from the loan, we have the PVA and the annuity payments and need to find
the interest rate, so:
76. To answer this, we need to diagram the perpetuity cash flows, which are: (Note, the subscripts are only
to differentiate when the cash flows begin. The cash flows are all the same amount.)
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So, we can write the cash flows as the present value of a perpetuity, and a perpetuity of:
77. We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant.
So, we can write the future value of a lump sum as:
CHAPTER 6 - 40
78. We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant.
So, we can write the future value of a lump sum with continuously compounded interest as:
