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chapter 4 analytical Flashcards

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1
Q

an investment pay you $30,000 at the end of this year, and $10,000 at the end of each of the following four years. what is the PV of this investment, given that the interest rate is 5% per year?

A

$79,228

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2
Q

a lottery winner will receive $6 million at the end of each of the next 12 years. what is the FV of her winnings at the time of her final payment, given that the interest rate is 8.6% per year?

A

$118 million

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3
Q

suppose you invest $1000 into a mutual fund that is expected to earn a rate of return or 11%. the amount of money you will have in ten years is closest to which of the following? the amount you will have in 50 years is closest to which of the following?

A

$2839; $184,565

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4
Q

consider the following timeline detailing a stream of cash flows. if the current market rate of interest is 10%, then the PV of this stream of cash flows is closest to ?

A

$20,227

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5
Q

consider the following timeline detailing a stream of cash flows. if the current market rate of interest is 8%, then the FV of this stream of cash flows is closest to ?

A

$11,699

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6
Q

consider the following timeline detailing a stream of cash flows. if the current market rate of interest is 8% then the PV of this stream of cash flows is closest to ?

A

$484

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7
Q

consider the following timeline detailing a stream of cash flows. if the current market rate of interest is 6%, then the FV of this stream of cash flows is closest to ?

A

$1723

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8
Q

if $8000 is invested in a certain business at the start of the year, the investor will receive $2400 at the end of each of the next four years. what is the PV of this business opportunity if the interest rate is 6% per year?

A

$316.25

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9
Q

a business premises to pay the investor of $6000 today for a payment of $1500 in one year’s time, $3000 in two years’ time, and $3000 in three years’ time. what is the PV of this business opportunity if the interest rate is 6% per year?

A

$603.94

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10
Q

salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. he must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. what is the PV of this investment if the interest rate is 3%?

A

$3189.80

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11
Q

a homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. after installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. how much must the homeowner save on water heating costs every year if this is to be a sound investment? (the interest rate is 5% per year)

A

$145

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12
Q

what is the PV of an investment that will pay $500 in one year’s time, and $500 every year after that, when the interest rate is 10%?

A

$5000

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13
Q

a perpetuity has a PV of $20,000. if the interest rate is 6%, how much will the perpetuity pay every year?

A

$1200

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14
Q

ally wishes to leave a provision in her will that $7000 will be paid annually in perpetuity to a local charity. how much must she provide in her will for this perpetuity if the interest rate is 6%?

A

$116,667

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15
Q

a perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. what is the PV of this perpetuity on the date that it is purchased, given that the interest rate is 11%?

A

$5390

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16
Q

a perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased. what is the FV of this perpetuity, given that the interest rate is 3%

A

there is no solution to this problem

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17
Q

an annuity is set up that will pay $1500 per year for ten years. what is the PV of this annuity given that the discount rate is 9%?

A

$9626

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18
Q

an annuity pays $10 per year for 98 years. what is the PV of this annuity given that the discount rate is 7%?

A

$142.67

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19
Q

an annuity pays $13 per year for 53 years. what is the FV of this annuity at the end of that 53 years given that the discount rate is 9%?

A

$13,764.85

20
Q

an annuity pays $47 per year for 22 years. what is the FV of this annuity at the end of those 22 years given that the discount rate is 8%?

A

$2606.47

21
Q

if the current rate of interest is 8%, then the PV of an investment that pays $1200 per year and lasts 24 years is closest to ?

A

$12,635

22
Q

if the current rate of interest is 7%, then the FV of an investment that pays $1200 per year and lasts 18 years is closest to ?

A

$40,799

23
Q

you are saving money to buy a car. if you save $310 per month starting one month from now at an interest rate of 6%, how much will you be able to spend on the car after saving for 4 years?

A

$16,770.33

24
Q

you are borrowing money to buy a car. if you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?

A

$12,151.67

25
Q

since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. the account pays 6% interest annually. immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ?

A

$37,086.78

26
Q

since your first birthday, your grandparents have been depositing $100 into a savings account every month. the account pays 9% interest annually. immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ?

A

$53,635

27
Q

clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. she wants the annual amount paid to the museum to grow by 5% per year. given that the interest rate is 9%, how much does she need to fund this perpetuity?

A

$250,000

28
Q

martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. the bequest will provide $4000 in the first year, and will grow by 7% per year, forever. if the interest rate is 9%, how much must martin provide to fund his bequest?

A

$200,000

29
Q

a rich donor gives a hospital $1,040,000 one year from today. each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in then years’ time. what is the PV of this donation, given that the interest rate is 11%?

A

$7,681,257.74

30
Q

which of the following statements regarding growing perpetuities is FALSE?

A

we assume that r < g for a growing perpetuity

31
Q

suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child’s college education. they decide to make deposits into an educational savings account on each of their daughter’s birthdays, starting with her first birthday. assume that the educational savings account will return to a constant 9%. the parents deposit $2400 on their daughter’s first birthday and plan to increase the size of their deposits by 7% each year. assuming that the parents have already made the deposit for their daughter’s 18th birthday, then the amount available for the daughter’s college expenses on her 18th birthday is closest to ?

A

$160,463

32
Q

suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child’s college education. currently, college tuition, books, fees, and other costs average $12,000 per year. on average, tuition and other costs have historically increased at a rate of 5% per year. assuming that college costs continue to increase an average of 5% per year and that all her college savings are invested in an account paying 8% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to ?

A

$110,793

33
Q

assume that you are 30 years old today, and that you are planning on retirement at age 65. your current salary is $42,000 and you expect your salary to increase at a rate of 5% per year as long as you work. to save for your retirement, you plan on making annual contributions to a retirement account. your first contribution will be made on your 31st birthday and will be 8% of this year’s salary. likewise, you expect to deposit 8% of your salary each year until you reach age 65. assume that the rate of interest is 9%. the PV at age 30 of your retirement savings is closest to ?

A

$61,303

34
Q

assume that you are 30 years old today, and that you are planning on retirement at age 65. your current salary is $40,000 and you expect your salary to increase at a rate of 5% per year as long as you work. to save for your retirement, you plan on making annual contributions to a retirement account. your first contribution will be made on your 31st birthday and will be 8% of this year’s salary. likewise, you expect to deposit 8% of your salary each year until you reach age 65. assume that the rate of interest is 10%. the FV at retirement (age 65) of your savings is closest to ?

A

$1,445,531

35
Q

you are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. as the ore closest to the surface is removed it will become more difficult to extract the ore. therefore, the value of the ore that you mine will decline at a rate of 7% per year forever. if the appropriate interest rate is 3%, then the value of this mining operation is closest to ?

A

$100,000

36
Q

dan buys a property for $210,000. he is offered a 30-year loan by the bank, at an interest rate of 8% per year. what is the annual loa payment dan must make?

A

$18,653.76

37
Q

a bank is negotiating a loan. the loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. if the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent?

A

$18,287

38
Q

a bank offers a home buyer a 20-year loan at 8% per year. if the home buyer borrows $130,000 from the bank, how much must be repaid every year?

A

$13,240.79

39
Q

matthew wants to take out a loan to buy a car he calculates that he can make repayments of $5000 per year. if he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?

A

$16,598

40
Q

a businessman wants to buy a truck. the dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. which of the following is closest to the interest rate being offered by the dealer?

A

6.8%

41
Q

how long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000?

A

4.25 years

42
Q

faisal has $12,000 in his savings account and can save an addition $3600 per year. if interest rates are 12%, how long will it take his savings to grow to $47,000?

A

5.3 years

43
Q

what is the internal rate of return of an investment that requires an initial investment of $11,000 today and pays $15,400 in one year’s time?

A

40%

44
Q

you are interested in purchasing a new automobile that costs $33,000. the dealership offers you a special financing rate of 9% APR (0.75% per month) for 60 months. assuming that you do not make a down payment on the auto and you take the dealer’s financing deal, then your monthly car payments would be closest to ?

A

$685

45
Q

you are considering purchasing a new home. you will need to borrow $290,000 to purchase the hoe. a mortgage company offers you a 20-year fixed rate mortgage (240 months) at 12% APR (1% month). if you borrow the money from this mortgage company, your monthly mortgage payment will be close to ?

A

$3193

46
Q

you are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. if the bond is currently selling for $496.97, then the internal rate of return for investing in this bond is closest to ?

A

6%

47
Q

you are offered an investment opportunity that costs you $28,000, has a net present value of $2278, lasts for three years, has interest rate of 10%, and produces the following cash flows. the missing cash flow from year 2 is closest to

A

$12,000

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